(*These are the PDE's for pde_in_cas web page in Mathematica syntax.*) (*Collected by Nasser M. Abbasi. These are the PDE used to make the webpage at *) (*https://www.12000.org/my_notes/pde_in_CAS/pde_in_cas.htm*) (*Any corrections, please report to nma@12000.org*) (*This file was last updated on Sun 12 May 2019 16:01:52 (*----------------------------*) (*PDE number 1*) ClearAll[u, x, t]; pde = D[u[x, t], {t}] + D[u[x, t], {x}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 2*) ClearAll[u, x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[3*D[u[x, y], x] + 5*D[u[x, y], y] == x, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 3*) ClearAll[u, x, y]; pde = x*D[u[x, y], y] + y*D[u[x, y], x] == -4*x*y*u[x, y]; ic = u[x, 0] == Exp[-x^2]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 4*) ClearAll[u, x, t]; pde = D[u[x, t], t] + D[u[x, t], x] == 0; bc = u[0, t] == 0; ic = u[x, 0] == Sin[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 5*) ClearAll[u, x, t, c]; ic = u[x, 0] == Exp[-x^2]; pde = D[u[x, t], {t}] + c*D[u[x, t], {x}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 6*) ClearAll[x, t, w]; pde = D[w[x, t], t] - 3*D[w[x, t], x] == 0; ic = w[x, 0] == Cos[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 7*) ClearAll[x, t, w, f, h]; pde = D[w[x, t], t] + c*D[w[x, t], x] == 0; ic = w[x, 0] == f[x]; bc = w[0, t] == h[t]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, w[x, t], {x, t}, Assumptions -> c > 0 && x > 0 && t > 0], 60*10]]; (*----------------------------*) (*PDE number 8*) ClearAll[x, t, w, f, h]; pde = D[w[x, t], t] + c*D[w[x, t], x] == Exp[2*x]; ic = w[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, ic}, w[x, t], {x, t}, Assumptions -> c > 0 && x > 0 && t > 0]], 60*10]]; (*----------------------------*) (*PDE number 9*) ClearAll[x, t, w, f]; pde = D[w[x, t], t] + 3*t*D[w[x, t], x] == w[x, t]; ic = w[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, ic}, w[x, t], {x, t}]], 60*10]]; (*----------------------------*) (*PDE number 10*) ClearAll[u, x, y]; pde = 2*D[u[x, y], x] + 5*D[u[x, y], y] == u[x, y]^2 + 1; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[pde, u[x, y], {x, y}]], 60*10]]; (*----------------------------*) (*PDE number 11*) ClearAll[u, x, y]; pde = D[u[x, y], {x}] + u[x, y]*D[u[x, y], {y}] == 0; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[pde, u[x, y], {x, y}]], 60*10]]; (*----------------------------*) (*PDE number 12*) ClearAll[u, x, y]; pde = D[u[x, y], {x}] + u[x, y]*D[u[x, y], {y}] == 0; ic = u[x, 0] == 1/(x + 1); sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, ic}, u[x, y], {x, y}]], 60*10]]; (*----------------------------*) (*PDE number 13*) ClearAll[u, x, y]; pde = u[x, y] == x*D[u[x, y], {x}] + y*D[u[x, y], {y}] + (1/2)*(D[u[x, y], {x}]^2 + D[u[x, y], {y}]^2); sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[pde, u[x, y], {x, y}]], 60*10]]; (*----------------------------*) (*PDE number 14*) ClearAll[u, x, y]; pde = u[x, y] == x*D[u[x, y], {x}] + y*D[u[x, y], {y}] + (1/2)*(D[u[x, y], {x}]^2 + D[u[x, y], {y}]^2); ic = u[x, 0] == (1*(1 - x^2))/2; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 15*) ClearAll[u, x, y]; pde = u[x, y] == x*D[u[x, y], x] + y*D[u[x, y], y] + Sin[D[u[x, y], x] + D[u[x, y], y]]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 16*) ClearAll[f, x, y]; eq1 = D[f[x, y], x] == x*y*Cos[x*y] + Sin[x*y]; eq2 = D[f[x, y], y] == -E^(-y) + x^2*Cos[x*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[{eq1, eq2}, f[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 17*) ClearAll[f, x, y, h, g]; pde = x*D[f[x, y], y] - D[f[x, y], x] == (f[x, y]^2*g[x])/h[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, f[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 18*) ClearAll[f, x, y, z]; pde = D[f[x, y, z], x] + D[f[x, y, z], y]^2 == f[x, y, z] + z; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, f[x, y, z], {x, y, z}], 60*10]]; (*----------------------------*) (*PDE number 19*) ClearAll[u, x, y, z]; pde = (y - z)*D[u[x, y, z], x] + (z - x)*D[u[x, y, z], y] + (x - y)*D[u[x, y, z], z] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y, z], {x, y, z}], 60*10]]; (*----------------------------*) (*PDE number 20*) ClearAll[u, t, k, x, L, n]; NumericQ[L] =. ; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[L, t] == 0}; ic = u[x, 0] == 6*Sin[(9*Pi*x)/L]; NumericQ[L] = True; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; NumericQ[L] =. ; (*----------------------------*) (*PDE number 21*) NumericQ[L] =. ; ClearAll[u, t, k, x, n]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[L, t] == 0}; ic = u[x, 0] == 3*Sin[(Pi*x)/L] - Sin[(3*Pi*x)/L]; NumericQ[L] = True; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; NumericQ[L] =. ; (*----------------------------*) (*PDE number 22*) ClearAll[u, t, k, x, L, n]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[L, t] == 0}; ic = u[x, 0] == 2*Cos[(3*Pi*x)/L]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> L > 0], 60*10]]; (*----------------------------*) (*PDE number 23*) ClearAll[u, t, k, x, L, n]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[L, t] == 0}; ic = u[x, 0] == Piecewise[{{1, Inequality[0, Less, x, LessEqual, L/2]}, {2, L/2 < x < L}}]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> L > 0], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 24*) ClearAll[u, t, k, x, L, sol, n, f]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {L > 0, k > 0, t > 0}], 60*10]]; sol = sol /. {K[1] -> n, K[2] -> x}; (*----------------------------*) (*PDE number 25*) ClearAll[u, t, k, x, L, a, f, alpha]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] - alpha*u[x, t]; bc = {u[0, t] == 0, u[L, t] == 0}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {L > 0, alpha > 0}], 60*10]]; (*----------------------------*) (*PDE number 26*) ClearAll[u, t, k, x, L]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = u[x, 0] == Piecewise[{{0, x < L/2}, {1, x > L/2}}]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {L > 0 && k > 0}], 60*10]]; sol = sol /. {K[1] -> n}; (*----------------------------*) (*PDE number 27*) NumericQ[L] =. ; ClearAll[u, t, k, x, L]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = u[x, 0] == 6 + 4*Cos[(3*Pi*x)/L]; NumericQ[L] = True; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; sol = sol /. {K[1] -> n}; NumericQ[L] =. ; (*----------------------------*) (*PDE number 28*) ClearAll[u, t, k, x, L]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = u[x, 0] == -2*Sin[(Pi*x)/L]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {L > 0 && k > 0}], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 29*) NumericQ[L] =. ; ClearAll[u, t, k, x, L]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = u[x, 0] == -3*Cos[(8*Pi*x)/L]; NumericQ[L] = True; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; sol = sol /. {K[1] -> n}; NumericQ[L] =. ; (*----------------------------*) (*PDE number 30*) ClearAll[u, t, k, x, L, f]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] == 0, u[L, t] == 0}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {L > 0 && k > 0}], 60*10]]; sol = sol /. {K[1] -> n, K[2] -> x}; (*----------------------------*) (*PDE number 31*) ClearAll[u, x, t, k]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; ic = u[x, 0] == 1 - (1*x^3)/4; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][1, t] == -u[1, t]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {k > 0, t > 0}], 60*10]]; (*----------------------------*) (*PDE number 32*) ClearAll[u, x, t, k, h, f]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; ic = u[x, 0] == f[x]; bc = {u[0, t] == 0, Derivative[1, 0][u][1, t] == -h u[1, t]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {k > 0, t > 0, h > 0}], 60*10]]; (*----------------------------*) (*PDE number 33*) ClearAll[u, x, t, k,h]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; ic = u[x, 0] == 0; bc = {Derivative[1, 0][u][0, t] == h * u[0,t], u[1, t] == 1}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions->h>0], 60*10]]; (*----------------------------*) (*PDE number 34*) ClearAll[u, t, x, L, c, f, k]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {u[-L, t] == u[L, t], Derivative[1, 0][u][-L, t] == Derivative[1, 0][u][L, t]}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> L > 0], 60*10]]; (*----------------------------*) (*PDE number 35*) NumericQ[L] =. ; ClearAll[u, t, x, k, L, f]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] + u[0, t] == 0, Derivative[1, 0][u][L, t] + u[L, t] == 0}; ic = u[x, 0] == f[x]; NumericQ[L] = True; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {t >= 0, k > 0, x >= 0, x <= L}], 60*10]]; NumericQ[L] =. ; (*----------------------------*) (*PDE number 36*) ClearAll[u, t, x, f]; pde = D[u[x, t], {t, 1}] == D[u[x, t], {x, 2}]; ic = u[x, 0] == f[x]; bc = {u[-1, t] == 0, u[1, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 37*) ClearAll[u, x, t, n]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; bc = {u[0, t] == 20, u[1, t] == 50}; ic = u[x, 0] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 38*) ClearAll[u, x, t, k, f, A, B, L, Q]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {u[0, t] == A, Derivative[1, 0][u][L, t] == B}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t, Assumptions -> L > 0], 60*10]]; (*----------------------------*) (*PDE number 39*) ClearAll[u, x, t, k, f, A0, B0, L0]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + k; bc = {u[0, t] == A0, u[L0, t] == B0}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 40*) ClearAll[x, t, u, f, L]; pde = D[u[x, t], t] + u[x, t] == D[u[x, t], {x, 2}]; ic = u[x, 0] == f[x]; bc = {u[0, t] == 0, u[L, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 41*) ClearAll[x, t, u, f, L]; f = Sin[2*Pi*x] - Sin[5*Pi*x]; pde = D[u[x, t], t] == 100*D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[1, t] == 0}; ic = u[x, 0] == f; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t][[1,1]], 60*10]]; (*----------------------------*) (*PDE number 42*) ClearAll[x, t, u, f, L, n]; f = Piecewise[{{x, Inequality[0, LessEqual, x, Less, 20]}, {40 - x, 20 <= x <= 40}}]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[40, t] == 0}; ic = u[x, 0] == f; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 43*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[1, t] == 0}; ic = u[x, 0] == Piecewise[{{0, x == 0}, {1, True}}]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; sol = sol /. {K[1] -> n} (*----------------------------*) (*PDE number 44*) ClearAll[u, t, x, n]; pde = D[u[x, t], {t, 1}] == D[u[x, t], {x, 2}]; bc = {u[0, t] == t, u[Pi, t] == 0}; ic = u[x, 0] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; sol = sol /. {K[1] -> n}; (*----------------------------*) (*PDE number 45*) ClearAll[u, x, t, k, f, L]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + Sin[(2*Pi*x)/L]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t, Assumptions -> {L > 0, k > 0, t > 0}], 60*10]]; (*----------------------------*) (*PDE number 46*) ClearAll[u, x, t, k, L]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + Cos[w*t]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = u[x, 0] == x; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t, Assumptions -> {L > 0, t > 0, k > 0}], 60*10]]; (*----------------------------*) (*PDE number 47*) ClearAll[u, x, t, k, f, L, c]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + Exp[-(c*t)]*Sin[(2*Pi*x)/L]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t, Assumptions -> {L > 0, k > 0, t > 0}], 60*10]]; (*----------------------------*) (*PDE number 48*) ClearAll[u, x, t, k, f, L, c]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] + t*(Pi-x); bc = {u[0,t] == 0, u[Pi,t] == 0}; ic = u[x, 0] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t, Assumptions -> t > 0], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 49*) pde = D[u[x, t], x] == D[u[x, t], {x, 2}] + 1 + x*Cos[t]; bc = {Derivative[1, 0][u][0, t] == Sin[t], Derivative[1, 0][u][1, t] == Sin[t]}; ic = u[x, 0] == 1 + Cos[2*Pi*x]; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, ic, bc}, u[x, t], x, t]], 60*10]]; (*----------------------------*) (*PDE number 50*) pde = D[u[x, t], x] == 13*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][1, t] == 1}; ic = u[x, 0] == (1*x^2)/2 + x; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 51*) ClearAll[u, t, x, f, g]; f[x] := 3*Cos[42*Pi*x]; g[x, t] := Exp[3*t]*Cos[17*x*Pi]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] + g[x, t]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][1, t] == 0}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 52*) ClearAll[u, t, x]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] + t*Cos[2001*x]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][Pi, t] == 0}; ic = u[x, 0] == Pi*Cos[2*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 53*) ClearAll[u, x, t, x]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] + x; bc = {u[0, t] == (t*Sin[t])/5, u[Pi, t] == (t*Cos[t])/10}; ic = u[x, 0] == 60 - 2*x; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t, Assumptions -> {t > 0, x > 0}], 60*10]]; (*----------------------------*) (*PDE number 54*) ClearAll[u, x, t, k, f, g, c]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + f[x, t]; bc = {u[0, t] == 0, u[1, t] == 0}; ic = u[x, 0] == g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t, Assumptions -> {k > 0, t > 0, x > 0, x < 1}], 60*10]]; (*----------------------------*) (*PDE number 55*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] + Sin[5*x]*Exp[-2*t]; bc = {u[0, t] == 1, u[Pi, t] == 0}; ic = u[x, 0] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 56*) ClearAll[u, x, t, k, f, A, B, L, Q]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + Q[x, t]; bc = {Derivative[1, 0][u][0, t] == A[t], Derivative[1, 0][u][L, t] == B[t]}; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t, Assumptions -> L > 0], 60*10]]; (*----------------------------*) (*PDE number 57*) ClearAll[u, x, t, k, n]; k = 1/20; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = {u[0, t] == 10, u[1, t] == 20}; ic = u[x, 0] == 60*x - 50*x^2 + 10; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 58*) ClearAll[u, x, t, k, n]; k = 1/20; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + t; bc = {u[0, t] == 5, u[1, t] + Derivative[1, 0][u][1, t] == 10}; ic = u[x, 0] == (-40*x^2)/3 + (45*x)/2 + 5; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 59*) ClearAll[u, x, t]; pde = D[u[x, t], t] == 13*D[u[x, t], {x, 2}]; bc = {Derivative[1, 0][u][0, t] == 0, Derivative[1, 0][u][1, t] == 1}; ic = u[x, 0] == (1*x^2)/2 + x; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 60*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] + (x - (1*x^2)/Pi); ic = u[x, 0] == Sin[x]; bc = {Derivative[1, 0][u][0, t] == 1, Derivative[1, 0][u][Pi, t] == -1}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 61*) ClearAll[u, x, t,A]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] ; ic = u[x, 0] == 0; bc = {u[0,t] == 0, Derivative[1, 0][u][Pi, t] == A}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t},Assumptions->A>0], 60*10]]; (*----------------------------*) (*PDE number 62*) ClearAll[u, x, t,A]; pde = D[u[r, t], t] == k*D[u[r, t], {r, 2}] ; ic = u[r, 0] == r*f[r]; bc = {u[0, t] == 0, u[a, t] == a*phi[t]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[r, t], {r, t}], 60*10]]; (*----------------------------*) (*PDE number 63*) ClearAll[u, x, t,h,b]; pde = D[u[x, t], t] == x^2*D[u[x, t], {x, 2}] + x*D[u[x, t], x]; ic = u[x, 0] == Log[x]; bc = {Derivative[1, 0][u][1, t] == 0, h*u[b, t] + Derivative[1, 0][u][b, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}, Assumptions -> {b > 1, t > 0, h > 0}], 60*10]]; (*----------------------------*) (*PDE number 64*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] - 9*D[u[x, t], x]; ic = u[x, 0] == Exp[45/10 x]*(5 Sin[Pi*x] + 9 Sin[2*Pi*x] + 2 Sin[3*Pi*x]); bc = {u[0, t] == 0, u[1, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 65*) ClearAll[u, x, t, f]; pde = D[u[x, t], t] == x^2*D[u[x, t], {x, 2}] + x*D[u[x, t], x]; ic = u[x, 0] == f[x]; bc = {u[1, t] == 0, u[b, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}, Assumptions -> b > 1], 60*10]]; (*----------------------------*) (*PDE number 66*) ClearAll[u, t, x, f]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; bc = u[0, t] == f[t]; ic = u[x, 0] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {t > 0, x > 0}], 60*10]]; sol = sol /. {K[2] -> z} (*----------------------------*) (*PDE number 67*) ClearAll[u, t, x, k]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = u[0, t] == 1; ic = u[x, 0] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {t > 0, k > 0, x > 0}], 60*10]]; (*----------------------------*) (*PDE number 68*) ClearAll[x, t, x0, t0]; pde = D[u[x, t], t] == (1/4)*D[u[x, t], {x, 2}]; bc = u[-x0, t] == 0; ic = u[x, t0] == 10; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], x, t, Assumptions -> {t > Abs[t0], x > Abs[x0]}], 60*10]]; (*----------------------------*) (*PDE number 69*) ClearAll[u, t, x, k, lambda, mu]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = u[0, t] == lambda; ic = u[x, 0] == mu; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {t > 0, k > 0, x > 0}], 60*10]]; (*----------------------------*) (*PDE number 70*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; ic = u[x, 0] == Cos[x]; bc = u[0, t] == 1; sol = AbsoluteTiming[TimeConstrained[FullSimplify[DSolve[{pde, ic, bc}, u[x, t], {x, t}]], 60*10]]; (*----------------------------*) (*PDE number 71*) ClearAll[u, x, t]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; ic = u[x, 0] == 0; bc = u[0, t] == t; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}, Assumptions -> {k > 0, x > 0, t > 0}], 60*10]]; (*----------------------------*) (*PDE number 72*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; ic = u[x, 0] == UnitTriangle[x - 3]; bc = Derivative[1, 0][u][0, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 73*) ClearAll[u, x, t, x0, t0]; pde = D[u[x, t], t] == (1*D[u[x, t], {x, 2}])/4; ic = u[x, t0] == 10*Exp[-x^2]; bc = Derivative[1, 0][u][x0, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}, Assumptions -> {x > 0, t > 0}], 60*10]]; (*----------------------------*) (*PDE number 74*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; ic = u[x, 0] == E^(-x^2); sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 75*) ClearAll[u, x, t]; pde = D[u[x, t], t] == 12*D[u[x, t], {x, 2}] + Sin[t]*D[u[x, t], x]; ic = u[x, 0] == x; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 76*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; ic = u[x, 0] == UnitBox[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 77*) ClearAll[u, t, x, m, k, f]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}, Assumptions -> {t > 0, k > 0}], 60*10]]; sol[[2]] = sol[[2]] /. K[1] -> s; (*----------------------------*) (*PDE number 78*) ClearAll[u, t, x, m, k]; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + m; ic = u[x, 0] == Sin[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 79*) ClearAll[x, y, t]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 80*) ClearAll[u, x, t, mu]; pde = D[u[x, t], t] + 1 == mu*D[u[x, t], {x, 2}]; ic = u[x, 1] == Piecewise[{{1, x <= 0}, {0, x > 0}}]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], x, t, Assumptions -> mu > 0], 60*10]]; (*----------------------------*) (*PDE number 81*) ClearAll[x, y, t]; pde = D[u[x, y, t], t] == (1*(D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}]))/10; ic = u[x, y, 0] == x*(1 - x)*(1 - y)*y; bc = {u[0, y, t] == 0, u[1, y, t] == 0, u[x, 0, t] == 0, u[x, 1, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 82*) ClearAll[x, y, t]; pde = D[u[x, y, t], t] == (1*(D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}]))/10 - (1*u[x, y, t])/5; ic = u[x, y, 0] == (-x^2 + 1)*(1 - (1/2)*y)*y; bc = {Derivative[1, 0, 0][u][0, y, t] == 0, u[1, y, t] == 0, u[x, 0, t] == 0, Derivative[0, 1, 0][u][x, 1, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 83*) ClearAll[x, y, t, k]; k = 1/50; pde = D[u[x, y, t], t] == k*(D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}]); bc = {Derivative[1, 0, 0][u][0, y, t] == 0, Derivative[1, 0, 0][u][1, y, t] + u[1, y, t] == 0, u[x, 0, t] == 0, u[x, 1, t] == 0}; ic = u[x, y, 0] == (1 - (1/3)*x^2)*y*(1 - y); sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 84*) ClearAll[r, t, u]; pde = D[u[r, t], t] == D[u[r, t], {r, 2}] + (1*D[u[r, t], r])/r; ic = u[r, 0] == 1 - r; bc = u[1, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[r, t], {r, t}], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 85*) ClearAll[r, t, u, k, a]; pde = D[u[r, t], t] == k*(D[u[r, t], {r, 2}] + D[u[r, t], r]/r) + f[r, t]; ic = u[r, 0] == 0; bc = u[a, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[r, t], {r, t}, Assumptions -> r < a], 60*10]]; (*----------------------------*) (*PDE number 86*) ClearAll[r, t, theta, u, k]; k = 1/50; pde = D[u[r, theta, t], t] == k*(D[u[r, theta, t], {r, 2}] + D[u[r, theta, t], r]/r + (1*D[u[r, theta, t], {theta, 2}])/r^2); bcOnR = u[1, theta, t] == 0; bcOnTheta = {u[r, 0, t] == 0, Derivative[0, 1, 0][u][r, Pi/2, t] == 0}; ic = u[r, theta, 0] == (r - (1*r^3)/3)*Sin[theta]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bcOnR, bcOnTheta, ic}, u[r, theta, t], {r, theta, t},Assumptions -> t > 0], 60*10]]; (*----------------------------*) (*PDE number 87*) ClearAll[r, t, theta, u, k]; k = 1/25; pde = D[u[r, theta, t], t] == k*(D[u[r, theta, t], {r, 2}] + D[u[r, theta, t], r]/r + (1*D[u[r, theta, t], {theta, 2}])/r^2); bcOnR = Derivative[1, 0, 0][u][1, theta, t] == 0; bcOnTheta = {u[r, 0, t] == 0, u[r, Pi, t] == 0}; ic = u[r, theta, 0] == (r - (1*r^3)/3)*Sin[theta]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bcOnR, bcOnTheta, ic}, u[r, theta, t], {r, theta, t}], 60*10]]; (*----------------------------*) (*PDE number 88*) ClearAll[r, t, theta, u, a, k, g, f]; pde = D[u[r, theta, t], t] == k*(D[u[r, theta, t], {r, 2}] + D[u[r, theta, t], r]/r + D[u[r, theta, t], {theta, 2}]/r^2); bcOnR = u[a, theta, t] == g[theta]; bcOnTheta = {u[r, -Pi, t] == u[r, Pi, t], Derivative[0, 1, 0][u][r, -Pi, t] == Derivative[0, 1, 0][u][r, Pi, t]}; ic = u[r, theta, 0] == f[r, theta]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bcOnR, bcOnTheta, ic}, u[r, theta, t], {r, theta, t}, Assumptions -> {a > 0, a < r, k > 0}], 60*10]]; (*----------------------------*) (*PDE number 89*) ClearAll[r, t, u, k]; pde = D[u[r, t], t] == (k*D[r*u[r, t], {r, 2}])/r; ic = u[r, 0] == 0; bc = u[1, t] == t; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[r, t], {r, t}, Assumptions -> {t > 0, k > 0}], 60*10]]; (*----------------------------*) (*PDE number 90*) ClearAll[x, t, k, r]; k = 1/10; r = 1; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + r*u[x, t]; bc = {u[0, t] == 0, u[1, t] == 0}; ic = u[x, 0] == 1; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 91*) ClearAll[x, t, k, r, alpha]; k = 1/100; r = 1/10; alpha = 10; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + r*u[x, t]*(1 - u[x, t]/alpha); bc = {u[0, t] == 0, u[1, t] == 0}; ic = u[x, 0] == 1; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 92*) ClearAll[x, t, k, alpha, beta, gamma]; k = 1/1000; alpha = 1/10; beta = 1/100; gamma = 5/1000; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}] + alpha*u[x, t] + beta*u[x, t]^2 - gamma*u[x, t]^3; bc = {u[0, t] == 0, u[1, t] == 0}; ic = u[x, 0] == 1; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 93*) ClearAll[x, t, f]; pde = D[u[x, t], t] == D[u[x, t], {x, 2}] - D[u[x, t], x]; ic = u[x, 0] == f[x]; bc = u[0, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}, Assumptions -> {x > 0, t > 0}], 60*10]]; (*----------------------------*) (*PDE number 94*) ClearAll[u, t, k, x, L, H, f]; pde = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0; bc = {Derivative[1, 0][u][0, y] == 0, Derivative[1, 0][u][L, y] == 0, u[x, 0] == 0, u[x, H] == f[x]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {0 <= x <= L && 0 <= y <= H}], 60*10]]; sol = sol /. {K[1] -> n}; (*----------------------------*) (*PDE number 95*) ClearAll[u, t, k, x, L, H, g, f]; pde = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0; bc = {Derivative[1, 0][u][0, y] == g[y], Derivative[1, 0][u][L, y] == 0, u[x, 0] == 0, u[x, H] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {0 <= x <= L && 0 <= y <= H}], 60*10]]; sol = sol /. {K[1] -> n}; (*----------------------------*) (*PDE number 96*) ClearAll[u, t, k, x, L, H, g, f]; pde = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0; bc = {Derivative[1, 0][u][0, y] == 0, u[L, y] == g[y], u[x, 0] == 0, u[x, H] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {0 <= x <= L && 0 <= y <= H}], 60*10]]; (*----------------------------*) (*PDE number 97*) ClearAll[u, x, L, H, g, f]; pde = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0; bc = {u[0, y] == 0, u[L, y] == 0, Derivative[0, 1][u][x, 0] == 0, u[x, H] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {0 <= x <= L && 0 <= y <= H}], 60*10]]; (*----------------------------*) (*PDE number 98*) ClearAll[u, x, L, H, g, f]; pde = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0; bc = {u[0, y] == 0, u[L, y] == 0, u[x, 0] - Derivative[0, 1][u][x, 0] == 0, u[x, H] == f[x]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {0 <= x <= L && 0 <= y <= H}], 60*10]]; (*----------------------------*) (*PDE number 99*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 0; L0 = 1; H0 = 2; bc = DirichletCondition[u[x, y] == Piecewise[{{UnitTriangle[2*x - L0], y == 0 || y == H0}}, 0], True]; domain = Rectangle[{0, 0}, {L0, H0}]; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, bc}, u[x, y], Element[{x, y}, domain]]], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 100*) ClearAll[u, x, y, L, A]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[0, y] == A, u[L, y] == 0, u[x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {x > 0, y > 0, L > 0}]], 60*10]]; (*----------------------------*) (*PDE number 101*) ClearAll[u, x, y, L, A]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[0, y] == 0, u[L, y] == A, u[x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {x > 0, y > 0, L > 0}]], 60*10]]; (*----------------------------*) (*PDE number 102*) ClearAll[u, x, y, L, A]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[0, y] == 0, u[x, 0] == A, u[x, L] == 0}; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {x > 0, y > 0, L > 0}]], 60*10]]; (*----------------------------*) (*PDE number 103*) ClearAll[u, x, y, L, A]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[0, y] == 0, u[x, L] == Exp[-x], u[x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {x > 0, y > 0, L > 0}]], 60*10]]; (*----------------------------*) (*PDE number 104*) ClearAll[u, x, y, L, A]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[0, y] == 0, u[x, 1] == f[x], u[x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {x > 0, y > 0}]], 60*10]]; (*----------------------------*) (*PDE number 105*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = u[x, 0] == DiracDelta[x]; sol = AbsoluteTiming[TimeConstrained[Simplify[DSolve[{pde, bc}, u[x, y], x, y]], 60*10]]; (*----------------------------*) (*PDE number 106*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[0, y] == 0, u[Pi, y] == Sinh[Pi]*Cos[y], u[x, 0] == Sin[x], u[x, Pi] == -Sinh[x]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], x, y], 60*10]]; (*----------------------------*) (*PDE number 107*) ClearAll[u, x, y]; pde = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0; bc = u[0, y] == Sin[y]/y; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> {0 <= x && 0 <= y}], 60*10]]; (*----------------------------*) (*PDE number 108*) ClearAll[x, y, a]; ode = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0; bc = {u[x, 0] == 0, u[x, a] == 0, u[0, y] == Sin[y], u[Infinity, y] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{ode, bc}, u[x, y], {x, y}, Assumptions -> a > 0], 60*10]]; (*----------------------------*) (*PDE number 109*) ClearAll[u, theta, r, a, f]; pde = D[u[r, theta], {r, 2}] + (1*D[u[r, theta], r])/r + (1*D[u[r, theta], {theta, 2}])/r^2 == 0; bc = u[a, theta] == f[theta]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[r, theta], {r, theta}, Assumptions -> a < r && a > 0 && Inequality[0, Less, theta, LessEqual, 2*Pi]], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 110*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = u[x, 0] == UnitBox[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 111*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = u[0, y] == Sinc[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 112*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[x, 0] == -((x - 2)^2 + 3)^(-1), u[0, y] == 1/((y - 3)^2 + 1)}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 113*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = Derivative[0, 1][u][x, 0] == UnitBox[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 114*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[x, 0] == x^2*(1 - x), u[x, 2] == 0, u[0, y] == 0, u[1, y] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; sol = sol /. K[1] -> n (*----------------------------*) (*PDE number 115*) ClearAll[u, x, y, h, b]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[x, 0] == 0, u[x, b] == h[x]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 116*) ClearAll[u, x, y, a]; pde = Laplacian[u[x, y], {x, y}] == 0; bc = {u[x, 0] == 0, u[x, a] == 0, u[0, y] == Sin[y], u[Infinity, y] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> a > 0], 60*10]]; (*----------------------------*) (*PDE number 117*) ClearAll[u, theta, r, f]; pde = D[u[r, theta], {r, 2}] + (1*D[u[r, theta], r])/r + (1*D[u[r, theta], {theta, 2}])/r^2 == 0; bcOnR = {Derivative[1, 0][u][1, theta] == f[theta]}; bcOnTheta = {u[r, 0] == 0, u[r, Pi/2] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bcOnR, bcOnTheta}, u[r, theta], {r, theta}, Assumptions -> {r > 0, r < 1, theta > 0, theta < Pi/2}], 60*10]]; (*----------------------------*) (*PDE number 118*) ClearAll[u, theta, r, f]; pde = D[u[r, theta], {r, 2}] + (1*D[u[r, theta], r]*1*D[u[r, theta], {theta, 2}])/(r*r^2) == 0; bc = {Derivative[1, 0][u][1, theta] == f[theta], u[r, Pi/2] == 0, u[r, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[r, theta], {r, theta}, Assumptions -> {0 <= r <= 1 && 0 <= theta <= Pi/2}], 60*10]]; (*----------------------------*) (*PDE number 119*) ClearAll[u, theta, r, f]; pde = D[u[r, theta], {r, 2}] + (1*D[u[r, theta], r]*1*D[u[r, theta], {theta, 2}])/(r*r^2) == 0; bc = {u[r, 0] == 0, u[r, Pi] == 0, u[0, theta] == 0, u[1, theta] == f[theta]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[r, theta], {r, theta}, Assumptions -> {0 <= r <= 1 && 0 <= theta <= Pi}], 60*10]]; (*----------------------------*) (*PDE number 120*) ClearAll[u, a, theta, r, g]; pde = D[u[r, theta], {r, 2}] + (1*D[u[r, theta], r])/r + (1*D[u[r, theta], {theta, 2}])/r^2 == 0; bc = {Derivative[1, 0][u][a, theta] == 0, u[b, theta] == g[theta]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[r, theta], {r, theta}, Assumptions -> Inequality[a, Less, r, LessEqual, b]], 60*10]]; (*----------------------------*) (*PDE number 121*) ClearAll[u, r, theta]; pde = D[u[r, theta], {r, 2}] + (1*D[u[r, theta], r])/r + (1*D[u[r, theta], {theta, 2}])/r^2 == 0; bc = {u[1, theta] == 0, u[2, theta] == Sin[theta]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[r, theta], {r, theta}], 60*10]]; (*----------------------------*) (*PDE number 122*) ClearAll[u, theta, r, a, f]; pde = D[u[r, theta], {r, 2}] + (1*D[u[r, theta], r])/r + (1*D[u[r, theta], {theta, 2}])/r^2 == 0; bc = {u[a, theta] == f[theta], u[r, -Pi] == u[r, Pi], Derivative[0, 1][u][r, -Pi] == Derivative[0, 1][u][r, Pi]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[r, theta], {r, theta}, Assumptions -> {a > 0, r > a}], 60*10]]; (*----------------------------*) (*PDE number 123*) ClearAll[u, \[Theta], \[Phi], r]; ClearAll[u, r, \[Theta], \[Phi]]; lap = Laplacian[f[r, \[Theta], \[Phi]], {r, \[Theta], \[Phi]}, "Spherical"]; sol = AbsoluteTiming[TimeConstrained[DSolve[lap == 0, f[r, \[Theta], \[Phi]], {r, \[Theta], \[Phi]}, Assumptions -> 0 <= \[Theta] <= Pi], 60*10]]; (*----------------------------*) (*PDE number 124*) ClearAll[a, b, A, B, theta, x, y, u]; pde = D[u[x, y], {x, 2}]/A + D[u[x, y], {y, 2}]/B == -2*theta; bc = {u[x, -b] == 0, u[x, b] == 0, u[-a, y] == 0, u[a, y] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 125*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] == 6*x - 6*y; bc = {u[x, 0] == 1 + 11*x + x^3, u[x, 2] == -7 + 11*x + x^3, u[0, y] == 1 - y^3, u[4, y] == 109 - y^3}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 126*) ClearAll[x, y, n, u]; pde = {Laplacian[u[x, y], {x, y}] + 5*u[x, y] == 0}; bc = {u[x, 0] == Piecewise[{{-1 + x, x > 1 && x < 2}, {3 - x, x > 2 && x < 3}}], u[x, 2] == 0, u[0, y] == 0, u[4, y] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; sol = sol /. K[1] -> n (*----------------------------*) (*PDE number 127*) ClearAll[x, y, n, u]; pde = {Laplacian[u[x, y], {x, y}] + 5*u[x, y] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 128*) ClearAll[x, y, n, u, k]; pde = Laplacian[u[x, y], {x, y}] - k*u[x, y] == 0; bc = {u[x, 0] == 0, u[x, Pi] == 0, u[0, y] == 1, u[Pi, y] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}, Assumptions -> k > 0], 60*10]]; (*----------------------------*) (*PDE number 129*) ClearAll[r,theta,U,k,lambda,t]; U = u[r, theta, t]; pde = D[U, t] == k*(lambda*U + (1/r^2)*D[r^2*D[U, r], r] + (1/(r^2*Sin[theta]))*D[Sin[theta]*D[U, theta], theta]); bc = u[R, theta, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, U, {r, theta, t}, Assumptions -> {k > 0, r < R}], 60*10]]; (*----------------------------*) (*PDE number 130*) ClearAll[u, x, t, k, L]; pde = D[u[x, t], {t, 2}] == D[u[x, t], {x, 2}] - u[x, t]; ic = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == 1}; bc = {u[0, t] == 0, u[Pi, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 131*) ClearAll[u, x, t, k, L]; pde = -D[u[x, t], {t, 2}] + u[x, t] == D[u[x, t], {x, 2}] + 2*Exp[-t]*(x - (1/2)*x^2 + (1/2)*t - 1); bc = {u[0, t] == 0, Derivative[1, 0][u][1, t] == 0}; ic = {u[x, 0] == x^2 - 2*x, u[x, 1] == u[x, 1/2] + ((1/2)*x^2 - x)*Exp[-1] - ((3*x^2)/4 - (3/2)*x)*Exp[-2^(-1)]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 132*) ClearAll[u, t, x, L, c]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[L, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, t], {x, t}, Assumptions -> {L > 0}], 60*10]]; (*----------------------------*) (*PDE number 133*) ClearAll[u, t, x, L, c, f]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, Derivative[1, 0][u][L, t] == 0}; ic = {Derivative[0, 1][u][x, 0] == 0, u[x, 0] == f[x]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {0 <= x <= L}], 60*10]]; (*----------------------------*) (*PDE number 134*) ClearAll[u, t, x, c, p]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}] + p[x, t]; bc = {u[0, t] == 0, u[Pi, t] == 0}; ic = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 135*) ClearAll[u, t, x, c, Q, L, f]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}] + Q[x, t]; bc = {u[0, t] == 0, u[L, t] == 0}; ic = {u[x, 0] == f[x], Derivative[0, 1][u][x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 136*) ClearAll[u, t, x, c, Q, L, f, g, w]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}] + g[x]*Cos[w*t]; bc = {u[0, t] == 0, u[L, t] == 0}; ic = {u[x, 0] == f[x], Derivative[0, 1][u][x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 137*) ClearAll[v, t, t]; pde = D[v[x, t], {t, 2}] == D[v[x, t], {x, 2}]; bc = {v[0, t] == 0, v[1, t] == 0}; ic = {v[x, 0] == -((Exp[2]*x - Exp[x + 1] - x + Exp[1 - x])/(Exp[2] - 1)), Derivative[0, 1][v][x, 0] == 1 + (Exp[2]*x - Exp[x + 1] - x + Exp[1 - x])/(Exp[2] - 1)}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, v[x, t], {x, t}], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 138*) ClearAll[u, t, x, c, L, f, g]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}] + 1; bc = {u[0, t] == 0, u[L, t] == 0}; ic = {u[x, 0] == f[x], Derivative[0, 1][u][x, 0] == g[x]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> L > 0], 60*10]]; (*----------------------------*) (*PDE number 139*) ClearAll[u, t, x, c, A, L]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}] + A*x; bc = {u[0, t] == 0, u[L, t] == 0}; ic = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 140*) pde = D[u[x, t], {t, 2}] + 2*D[u[x, t], t] == D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[Pi, t] == 0}; ic = {Derivative[0, 1][u][x, 0] == 0, u[x, 0] == f[x]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 141*) ClearAll[a, u, x, t, gamma]; pde = (1*D[u[x, t], {t, 2}])/a^2 + gamma^2*u[x, t] == D[u[x, t], {x, 2}]; bc = {u[0, t] == 0, u[Pi, t] == 0}; ic = {Derivative[0, 1][u][x, 0] == 0, u[x, 0] == Sin[x]^2}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 142*) ClearAll[u, t, x, n]; pde = D[u[x, t], {t, 2}] == 4*D[u[x, t], {x, 2}]; ic = {Derivative[0, 1][u][x, 0] == 0, u[x, 0] == Sin[x]^2}; bc = {u[0, t] == 0, u[Pi, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 143*) ClearAll[u, t, x]; pde = D[u[x, t], {t, 2}] == D[u[x, t], {x, 2}] + x*Exp[-t]; ic = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == 0}; bc = {u[0, t] == 0, u[1, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 144*) ClearAll[u, t, x]; pde = D[u[x, t], {t, 2}] == 4*D[u[x, t], {x, 2}] + (1 + t)*x; ic = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == 0}; bc = {u[0, t] == 0, u[Pi, t] == Sin[t]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 145*) ClearAll[u, t, x, g, c]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}] - g; bc = u[0, t] == 0; ic = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {t > 0 && c > 0 && x > 0}], 60*10]]; (*----------------------------*) (*PDE number 146*) ClearAll[u, t, x, g, c]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}]; bc = u[0, t] == g[t]; ic = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, t], {x, t}, Assumptions -> {t > 0 && c > 0 && x > 0}], 60*10]]; (*----------------------------*) (*PDE number 147*) ClearAll[u, t, x]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}]; ic = {u[x, 0] == Piecewise[{{Sin[x]^2, Pi < x < 2*Pi}}], Derivative[0, 1][u][x, 0] == 0}; bc = u[0, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 148*) ClearAll[u, t, x]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}]; ic = {u[x, 0] == Sin[x]^3, Derivative[0, 1][u][x, 0] == 1 - E^(-(x/10))}; bc = Derivative[1, 0][u][0, t] == 1; sol = AbsoluteTiming[TimeConstrained[DSolveValue[{pde, ic, bc}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 149*) ClearAll[u, t, x]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}]; ic = {u[x, 0] == Sin[x]^3, Derivative[0, 1][u][x, 0] == 1 - E^(-(x/10))}; bc = Derivative[1, 0][u][0, t] == 1; sol = AbsoluteTiming[TimeConstrained[DSolveValue[{pde, ic, bc}, u[x, t], {x, t}, Assumptions -> t > 0], 60*10]]; (*----------------------------*) (*PDE number 150*) ClearAll[u, t, x]; pde = D[u[x, t], {t, 2}] == (1*D[u[x, t], {x, 2}])/4; ic = {u[x, 0] == Exp[-x^2], Derivative[0, 1][u][x, 0] == 0}; bc = Derivative[1, 0][u][1, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}, Assumptions -> {t > 0, x > 0}], 60*10]]; (*----------------------------*) (*PDE number 151*) ClearAll[u, t, x, c, h, f, g]; pde = D[u[x, t], {t, 2}] == c^2*D[u[x, t], {x, 2}]; ic = {u[x, 1] == g[x], Derivative[0, 1][u][x, 1] == h[x]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}, Assumptions -> {t > 0, x > 0}], 60*10]]; (*----------------------------*) (*PDE number 152*) ClearAll[u, t, x]; pde = D[u[x, t], {t, 2}] == 9*D[u[x, t], {x, 2}]; ic = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == x^3}; bc = Derivative[1, 0][u][0, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], {x, t}, Assumptions -> {t > 0, x > 0}], 60*10]]; (*----------------------------*) (*PDE number 153*) ClearAll[u, t, x, c]; ode = D[u[x, t], {t, 2}] + D[u[x, t], x, t] == c^2*D[u[x, t], {x, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[ode, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 154*) ClearAll[u, t, x]; pde = D[u[x, t], {t, 2}] == D[u[x, t], {x, 2}]; ic = {u[x, 0] == E^(-x^2), Derivative[0, 1][u][x, 0] == 1}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 155*) ClearAll[u, t, x]; pde = {D[u[x, t], {t, 2}] == D[u[x, t], {x, 2}] + m}; ic = {u[x, 0] == Sin[x] - Cos[3*x]/E^(Abs[x]/6), Derivative[0, 1][u][x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 156*) ClearAll[u, t, x]; pde = D[u[x, t], t] + 6*u[x, t]*D[u[x, t], x] + D[u[x, t], {x, 3}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 157*) ClearAll[u, x, y]; ode = D[u[x, y], {x, 2}] - 2*Sin[x]*D[u[x, y], x, y] - Cos[x]^2*D[u[x, y], {y, 2}] - Cos[x]*D[u[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[ode, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 158*) ClearAll[u, x, t]; ode = 3*D[u[x, t], {x, 2}] - D[u[x, t], {t, 2}] + D[u[x, t], x, t] == 1; sol = AbsoluteTiming[TimeConstrained[DSolve[ode, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 159*) ClearAll[u, v, x, t]; eqns = {D[u[x, t], t] == D[v[x, t], x] + 1, D[v[x, t], t] == -D[u[x, t], x] - 1}; ic = {u[x, 0] == Cos[x]^2, v[x, 0] == Sin[x]}; sol = AbsoluteTiming[TimeConstrained[FullSimplify[DSolve[{eqns, ic}, {u[x, t], v[x, t]}, {x, t}]], 60*10]]; (*----------------------------*) (*PDE number 160*) ClearAll[u, t, y, x]; pde = D[u[x, y, t], {t, 2}] == (1*(D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}]))/4; ic = {Derivative[0, 0, 1][u][x, y, 0] == 0, u[x, y, 0] == x*y*(Pi - y)}; bc = {Derivative[1, 0, 0][u][0, y, t] == 0, Derivative[1, 0, 0][u][Pi, y, t] == 0, u[x, 0, t] == 0, u[x, Pi, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 161*) ClearAll[u, t, y, x]; pde = D[u[x, y, t], {t, 2}] == (1*(D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}]))/4 - (1*D[u[x, y, t], t])/10; ic = {u[x, y, 0] == 0, Derivative[0, 0, 1][u][x, y, 0] == x*(1 - (1/2)*x)*(1 - (1/2)*y)*y}; bc = {u[0, y, t] == 0, Derivative[1, 0, 0][u][1, y, t] == 0, u[x, 0, t] == 0, Derivative[0, 1, 0][u][x, 1, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 162*) ClearAll[u, t, y, x, n, m]; pde = D[u[x, y, t], {t, 2}] == Laplacian[u[x, y, t], {x, y}]; ic = {u[x, y, 0] == (1/10)*(x - x^2)*(2*y - y^2), Derivative[0, 0, 1][u][x, y, 0] == 0}; bc = {u[x, 0, t] == 0, u[0, y, t] == 0, u[1, y, t] == 0, u[x, 2, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, y, t], {x, y, t}], 60*10]]; sol = sol /. {K[1] -> n, K[2] -> m}; sol = Assuming[Element[{n, m}, Integers], FullSimplify[sol]]; (*----------------------------*) (*PDE number 163*) ClearAll[u, t, y, x, n, m, L, H, Q, f]; pde = D[u[x, y, t], {t, 2}] == c^2*Laplacian[u[x, y, t], {x, y}] + Q[x, y, t]; ic = {u[x, y, 0] == f[x, y], Derivative[0, 0, 1][u][x, y, 0] == 0}; bc = {u[0, y, t] == 0, u[L, y, t] == 0, u[x, 0, t] == 0, u[x, H, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, y, t], {x, y, t}, Assumptions -> {L > 0, H > 0, t > 0, c > 0}], 60*10]]; (*----------------------------*) (*PDE number 164*) ClearAll[u, t, r, n]; pde = D[u[r, t], {t, 2}] == c^2*(D[u[r, t], {r, 2}] + (1*D[u[r, t], r])/r); ic = {u[r, 0] == 1, Derivative[0, 1][u][r, 0] == r/3}; bc = u[1, t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[r, t], {r, t}], 60*10]]; sol = sol /. K[1] -> n; sol = FullSimplify[sol]; (*----------------------------*) (*PDE number 165*) ClearAll[u, t, r, n, theta, a, f]; pde = D[u[r, theta, t], {t, 2}] == c^2*(D[u[r, theta, t], {r, 2}] + (1*D[u[r, theta, t], r])/r + (1*D[u[r, theta, t], {theta, 2}])/r^2); ic = {u[r, theta, 0] == f[r, theta], Derivative[0, 0, 1][u][r, theta, 0] == 0}; bc = {u[a, theta, t] == 0, u[r, -Pi, t] == u[r, Pi, t], Derivative[0, 1, 0][u][r, -Pi, t] == Derivative[0, 1, 0][u][r, Pi, t]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[r, theta, t], {r, theta, t}, Assumptions -> {0 < r < a, a > 0, t > 0, -Pi < theta < Pi}], 60*10]]; (*----------------------------*) (*PDE number 166*) ClearAll[u, t, r, theta, phi]; lap = Laplacian[u[r, theta, phi, t], {r, theta, phi}, "Spherical"]; pde = D[u[r, theta, phi, t], {t, 2}] == c^2*lap; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[r, theta, phi, t], {r, theta, phi, t}, Assumptions -> {0 < theta < Pi}], 60*10]]; (*----------------------------*) (*PDE number 167*) ClearAll[u, t, r, z, phi]; lap = Laplacian[u[r, phi, z, t], {r, phi, z}, "Cylindrical"]; pde = D[u[r, phi, z, t], {t, 2}] == c^2*lap; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[r, phi, z, t], {r, phi, z, t}], 60*10]]; (*----------------------------*) (*PDE number 168*) ClearAll[f, t, x, L, m, h]; pde = I*h*D[f[x, t], t] == -((h^2*D[f[x, t], {x, 2}])/(2*m)); bc = {f[0, t] == 0, f[L, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, f[x, t], {x, t}, Assumptions -> L > 0], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 169*) ClearAll[f, t, x, y]; pde = I*D[f[x, y, t], {t}] == -((hBar^2*Laplacian[f[x, y, t], {x, y}])/(2*m)); initSum = f[x, y, 0] == Sqrt[2]*(Sin[2*Pi*x]*Sin[Pi*y] + Sin[Pi*x]*Sin[2*Pi*y]); bcs = {f[0, y, t] == 0, f[1, y, t] == 0, f[x, 1, t] == 0, f[x, 0, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bcs, initSum}, f[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 170*) ClearAll[g, f, t, x]; pde = I*D[f[x, t], t] == -2*D[f[x, t], {x, 2}]; g[x_] := -350 + 155*x - 22*x^2 + x^3; ic = f[x, 2] == g[x]; bc = {f[5, t] == 0, f[10, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc, ic}, f[x, t], {x, t}], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 171*) ClearAll[f, t, x]; pde = I*D[f[x, t], t] == -D[f[x, t], {x, 2}] + 2*x^2*f[x, t]; bc = {f[-Infinity, t] == 0, f[Infinity, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, f[x, t], {x, t}], 60*10]]; sol = sol /. K[1] -> n; (*----------------------------*) (*PDE number 172*) ClearAll[x, t, f, a, A, m, h]; ic = Piecewise[{{A*x*(a - x), 0 <= x <= a}, {0, True}}]; pde = I*h*D[f[x, t], t] == -((h^2*D[f[x, t], {x, 2}])/(2*m)); sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, f[x, 0] == ic}, f[x, t], {x, t}, Assumptions -> a > 0], 60*10]]; (*----------------------------*) (*PDE number 173*) ClearAll[x, y, t, f, m]; ic = f[x, y, 0] == Sqrt[2]*(Sin[2*Pi*x]*Sin[Pi*y] + Sin[Pi*x]*Sin[3*Pi*y]); bc = {f[0, y, t] == 0, f[1, y, t] == 0, f[x, 1, t] == 0, f[x, 0, t] == 0}; pde = I*h*D[f[x, y, t], t] == -((h^2*(D[f[x, y, t], {x, 2}] + D[f[x, y, t], {y, 2}]))/(2*m)); sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, f[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 174*) ClearAll[x, t, f, a, A, m, h]; v[x_] = Piecewise[{{0, 0 <= x <= a}}, Infinity]; ic = Piecewise[{{A*x*(a - x), 0 <= x <= a}, {0, True}}]; ode = I*h*D[f[x, t], t] == -((h^2*D[f[x, t], {x, 2}])/(2*m)) + v[x]*f[x, t]; sol = AbsoluteTiming[TimeConstrained[DSolve[{ode, f[x, 0] == ic}, f[x, t], {x, t}, Assumptions -> a > 0], 60*10]]; (*----------------------------*) (*PDE number 175*) ClearAll[u, x, t]; pde = D[u[x, t], {t, 2}] + D[u[x, t], {x, 4}] == 0; bc = {u[0, t] == -12*t^2, u[1, t] == 1 - 12*t^2, Derivative[2, 0][u][0, t] == 0, Derivative[2, 0][u][1, t] == 12}; ic = {u[x, 0] == x^4, Derivative[0, 1][u][x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[x, t], x, t], 60*10]]; (*----------------------------*) (*PDE number 176*) ClearAll[u, x, t, mu]; pde = D[u[x, t], {t}] + u[x, t]*D[u[x, t], {x}] == \[Mu]*D[u[x, t], {x, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 177*) ClearAll[u, x, y, mu]; pde = D[u[x, t], {t}] + u[x, t]*D[u[x, t], {x}] == mu*D[u[x, t], {x, 2}]; ic = u[x, 0] == Piecewise[{{1, x < 0}, {0, x >= 1}}]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}, Assumptions -> mu > 0], 60*10]]; (*----------------------------*) (*PDE number 178*) ClearAll[u, x, y, mu]; pde = D[u[x, t], {t}] + u[x, t]*D[u[x, t], {x}] == mu*D[u[x, t], {x, 2}]; ic = u[x, 0] == UnitBox[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 179*) ClearAll[u, t, x, sigma, k]; pde = D[u[x, t], t] == (1*sigma^2*D[u[x, t], {x, 2}])/2; ic = u[x, 0] == k*Exp[x - 1]*HeavisideTheta[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}, Assumptions -> k > 0], 60*10]]; (*----------------------------*) (*PDE number 180*) ClearAll[t, s, v, sigma, psi]; pde = D[v[t, s], t] + (1*sigma^2*s^2*D[v[t, s], {s, 2}])/2 + (r - q)*s*D[v[t, s], s] - r*v[t, s] == 0; bc = v[T, s] == psi[s]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, v[t, s], {t, s}], 60*10]]; (*----------------------------*) (*PDE number 181*) ClearAll[u, x, t]; pde = D[u[x, t], {x, 3}] + D[u[x, t], {t}] - 6*u[x, t]*D[u[x, t], {x}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 182*) ClearAll[u, x, y]; pde = D[u[x, y], {x, 2}] + y*D[u[x, y], {y, 2}] == 0; bc = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == x^2}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 183*) ClearAll[u, v, x, y]; pde1 = D[u[x, y], x] == D[v[x, y], y]; pde2 = D[u[x, y], y] == -D[v[x, y], x]; bc = {u[x, 0] == x^3, v[x, 0] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde1, pde2, bc}, {u[x, y], v[x, y]}, {x, y}], 60*10]]; (*----------------------------*) (*PDE number 184*) ClearAll[u, v, x, y]; pde1 = D[u[x, y], x] == D[v[x, y], y]; pde2 = D[u[x, y], y] == -D[v[x, y], x] + y; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde1, pde2}, {u[x, y], v[x, y]}, {x, y}], 60*10]]; (*----------------------------*) (*PDE number 185*) ClearAll[t, \[Zeta], \[Eta], \[Phi], a, b, s]; pde = -D[s[t, \[Zeta], \[Eta], \[Phi]], t] == ((\[Zeta]^2 - 1)*D[s[t, \[Zeta], \[Eta], \[Phi]], \[Zeta]]^2)/(2*\[Sigma]^2*m*(-\[Eta]^2 + \[Zeta]^2)) + ((-\[Eta]^2 - 1)*D[s[t, \[Zeta], \[Eta], \[Phi]], \[Eta]]^2)/(2*\[Sigma]^2*m*(-\[Eta]^2 + \[Zeta]^2)) + (1*D[s[t, \[Zeta], \[Eta], \[Phi]], \[Phi]]^2)/(2*\[Sigma]^2*m*(\[Zeta]^2 - 1)*(-\[Eta]^2 - 1)) + (a[\[Zeta]] + b[\[Zeta]])/(-\[Eta]^2 + \[Zeta]^2); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, s[t, \[Zeta], \[Eta], \[Phi]], {t, \[Zeta], \[Eta], \[Phi]}], 60*10]]; (*----------------------------*) (*PDE number 186*) ClearAll[s, x, y]; pde = s[x, y]*D[s[x, y], x, y] + D[s[x, y], x]*D[s[x, y], y] == 1; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, s[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 187*) ClearAll[u, r, theta]; pde = D[u[r, theta], {r, 2}] + D[u[r, theta], {theta, 2}] == 0; bc = u[2, theta] == 3*Sin[2*theta] + 1; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[r, theta], {r, theta}], 60*10]]; (*----------------------------*) (*PDE number 188*) ClearAll[u, x, y]; pde = D[u[x, y], {x, 2}] + y*D[u[x, y], {y, 2}] == 0; bc = {u[x, 0] == 0, Derivative[0, 1][u][x, 0] == x^2}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 189*) ClearAll[u, x, t, f]; pde = D[u[x, t], t] == -D[u[x, t], {x, 3}]; ic = u[x, 0] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 190*) ClearAll[u, x, y]; pde = D[u[x, y], y, x] == Sin[x]*Sin[y]; bc = {u[x, 0] == 1 + Cos[x], Derivative[0, 1][u][0, y] == -2*Sin[y]}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, u[x, y], x, y], 60*10]]; (*----------------------------*) (*PDE number 191*) ClearAll[w, x1, x2, x3, t, a]; pde = D[w[x1, x2, x3, t], t] == D[w[x1, x2, x3, t], {x1, 2}] + D[w[x1, x2, x3, t], {x2, 2}] + D[w[x1, x2, x3, t], {x3, 2}]; ic = w[x1, x2, x3, 1] == Exp[a]*x1^2 + x2*x3; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, w[x1, x2, x3, t], {x1, x2, x3, t}], 60*10]]; (*----------------------------*) (*PDE number 192*) ClearAll[w, x1, x2, x3, t, t0]; pde = D[w[x1, x2, x3, t], t] == D[w[x1, x2, x3, t], x1, x2] + D[w[x1, x2, x3, t], x1, x3] + D[w[x1, x2, x3, t], {x3, 2}] - D[w[x1, x2, x3, t], x2, x3]; ic = w[x1, x2, x3, t0] == Exp[x1] + x2 - 3*x3; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, w[x1, x2, x3, t], {x1, x2, x3, t}], 60*10]]; (*----------------------------*) (*PDE number 193*) ClearAll[w, x1, x2, x3, t, t0]; pde = D[w[x1, x2, x3, t], {t, 2}] == D[w[x1, x2, x3, t], x1, x2] + D[w[x1, x2, x3, t], x1, x3] + D[w[x1, x2, x3, t], {x3, 2}] - D[w[x1, x2, x3, t], x2, x3]; ic = {w[x1, x2, x3, t0] == x1^3*x2^2 + x3, Derivative[0, 0, 0, 1][w][x1, x2, x3, t0] == -(x2*x3) + x1}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, w[x1, x2, x3, t], {x1, x2, x3, t}], 60*10]]; (*----------------------------*) (*PDE number 194*) ClearAll[u, x, t, beta, d]; pde = D[u[x, t], t] == beta*D[u[x, t], x] + d*D[u[x, t], {x, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}, Assumptions -> {beta > 0, d > 0, x > 0, t > 0}], 60*10]]; (*----------------------------*) (*PDE number 195*) ClearAll[u, x, t, v]; pde = D[u[x, t], t] + u[x, t]*D[u[x, t], x] == v*D[u[x, t], {x, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 196*) ClearAll[u, x, t]; pde = D[u[x, t], t] + D[u[x, t], x] + u[x, t]*D[u[x, t], x] - D[D[u[x, t], {x, 2}], t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 197*) ClearAll[u, x, t, h]; pde = D[u[x, t], t] + h*D[u[x, t], {x, 2}] + u[x, t]*D[u[x, t], x] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 198*) ClearAll[u, x, t]; pde = (1 - D[u[x, t], t]^2)*D[u[x, t], {x, 2}] + 2*D[u[x, t], x]*D[u[x, t], t]*D[D[u[x, t], x], t] - (1 + D[u[x, t], x]^2)*D[u[x, t], {t, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 199*) ClearAll[u, x, t]; pde = D[u[x, t], {t, 2}] - D[u[x, t], {x, 2}] - D[u[x, t], {x, 4}] - 3*D[u[x, t]^2, {x, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 200*) ClearAll[u, x, t]; pde = D[u[x, t], {t, 2}] - D[u[x, t], {x, 2}] - D[u[x, t], {x, 4}] - 3*D[u[x, t]^2, {x, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 201*) ClearAll[u, x, t]; pde = D[u[x, t], t] == D[u[x, t]^4, {x, 2}] + D[u[x, t]^3, x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 202*) ClearAll[u, x, t, k]; pde = D[u[x, t], t] + 2*k*D[u[x, t], x] - D[D[u[x, t], {x, 2}], t] + 3*u[x, t]*D[u[x, t], x] == 2*D[u[x, t], x]*D[u[x, t], {x, 2}] + u[x, t]*D[u[x, t], {x, 3}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 203*) ClearAll[u, x, t, lambda]; pde = D[u[x, t], t] - D[u[x, t], {x, 2}] + lambda*(u[x, t]^3 - u[x, t]) == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 204*) ClearAll[theta, x, t, gamma]; pde = D[D[theta[x, t], t] - gamma*Exp[theta[x, t]], {t, 2}] == D[D[theta[x, t], t] - Exp[theta[x, t]], {x, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, theta[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 205*) ClearAll[u, x, t]; pde = D[u[x, t], t] - D[D[u[x, t], {x, 2}], t] + 4*u[x, t]*D[u[x, t], x] == 3*D[u[x, t], x]*D[u[x, t], {x, 2}] + u[x, t]*D[u[x, t], {x, 3}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 206*) ClearAll[u, x, t]; pde = D[u[x, t], t] == u[x, t]^3*D[u[x, t], {x, 3}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 207*) ClearAll[u, x, t, y, beta]; pde = D[D[u[x, y, t], t], {y, 3}] + beta*D[u[x, y, t], y]*D[D[u[x, y, t], y], t] + beta*D[u[x, y, t], {y, 2}]*D[u[x, y, t], t] + D[u[x, y, t], {t, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 208*) ClearAll[u, x, t]; pde = D[u[x, t], t] == u[x, t]*(1 - u[x, t]) + D[u[x, t], {x, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 209*) ClearAll[u, x, t]; pde = D[D[u[x, t], t] + u[x, t]*D[u[x, t], x], x] == (1*D[u[x, t], x]^2)/2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 210*) ClearAll[u, x, t]; pde = D[D[u[x, y, t], t] + u[x, y, t]*D[u[x, y, t], x] + eps^2*D[u[x, y, t], {x, 3}], t] + lambda*D[u[x, y, t], {y, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 211*) ClearAll[u, x, y, lambda]; pde = Laplacian[u[x, y], {x, y}] + lambda*u[x, y]^p == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 212*) ClearAll[u, x, y, lambda]; pde = Laplacian[u[x, y], {x, y}] + u[x, y]^2 == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 213*) ClearAll[u, x, y, t]; pde = D[D[u[x, y, t], x], t] - D[u[x, y, t]*D[u[x, y, t], x], x] == D[u[x, y, t], {y, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 214*) ClearAll[u, x, t]; pde = D[u[x, t], t] + D[u[x, t], x]^3 + 6*u[x, t]*D[u[x, t], x] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 215*) ClearAll[u, x, t]; pde = 2*D[u[x, y, t], t, x] + D[u[x, y, t], x]*D[u[x, y, t], {x, 2}] - D[u[x, y, t], {y, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y, t], {x, y, t}], 60*10]]; (*----------------------------*) (*PDE number 216*) ClearAll[u, x, lam, y]; pde = Laplacian[u[x, y], {x, y}] + Exp[lam*u[x, y]] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 217*) ClearAll[u, x, y]; pde = (1 + D[u[x, y], y]^2)*D[u[x, y], {x, 2}] - 2*D[u[x, y], x]*D[u[x, y], y]*D[u[x, y], x, y] + (1 + D[u[x, y], x]^2)*D[u[x, y], {y, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 218*) ClearAll[u, x, t, epsilon]; pde = D[u[x, t], {t, 2}] - D[u[x, t], {x, 2}] == epsilon*(D[u[x, t], t] - D[u[x, t], t]^3); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 219*) ClearAll[phi, x, t]; pde = D[u[x, t], t] + 45*u[x, t]^2*D[u[x, t], x] + 15*D[u[x, t], x]*D[u[x, t], {x, 2}] + 15*u[x, t]*D[u[x, t], {x, 3}] + D[u[x, t], {x, 5}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 220*) ClearAll[phi, x, t]; pde = D[phi[x, t], {t, 2}] - D[phi[x, t], {x, 2}] + Sin[phi[x, t]] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, phi[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 221*) ClearAll[u, x, t]; pde = D[u[x, t], x, t] == Sinh[u[x, t]]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 222*) ClearAll[u, x, y]; pde = Laplacian[u[x, y], {x, y}] + Sinh[u[x, y]] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 223*) ClearAll[u, x, y, alpha, beta, nu]; pde = D[u[x, y], x, y] + alpha*D[u[x, y], x] + beta*D[u[x, y], y] + nu*D[u[x, y], x]*D[u[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 224*) ClearAll[u, x, y, alpha, beta, nu]; pde = D[phi[x, t], t, t] - D[phi[x, t], x, x] - phi[x, t] + phi[x, t]^3 == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, phi[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 225*) ClearAll[w, x, y, f]; pde = D[w[x, y], x] == f[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 226*) ClearAll[w, x, y, f]; pde = D[w[x, y], y] == f[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 227*) ClearAll[w, x, y, f]; pde = D[w[x, y], x] == w[x, y]*f[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 228*) ClearAll[w, x, y, f]; pde = D[w[x, y], y] == w[x, y]*f[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 229*) ClearAll[w, x, y, f, g]; pde = D[w[x, y], x] == w[x, y]*f[x, y] + g[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 230*) ClearAll[w, x, y, f, g]; pde = D[w[x, y], y] == w[x, y]*f[x, y] + g[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 231*) ClearAll[w, x, y, a, b]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 232*) ClearAll[w, x, y, a, b, c]; pde = a*D[w[x, y], x] + (b*x + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 233*) ClearAll[w, x, y, a, b, c]; pde = D[w[x, y], x] + (a*x + b*y + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 234*) ClearAll[w, x, y, a, b, c]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 235*) ClearAll[w, x, y, a, b]; pde = a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 236*) ClearAll[w, x, y, a]; pde = y*D[w[x, y], x] + (y + a)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 237*) ClearAll[w, x, y, a, b, c, s]; pde = (a*y + b*x + c)*D[w[x, y], x] - (b*y + k*x + s)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 238*) ClearAll[w, x, y, a1, a2, b1, b2, c1, c2]; pde = (a1*x + b1*y + c1)*D[w[x, y], x] + (a1*x + b2*y + c2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 239*) ClearAll[w, x, y, a, b, c]; pde = D[w[x, y], x] + (a*x^2 + b*x + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 240*) ClearAll[w, x, y, a, b, c]; pde = D[w[x, y], x] + (a*y^2 + b*y + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 241*) ClearAll[w, x, y, a, b, c]; pde = D[w[x, y], x] + (a*y + b*x^2 + c*x)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 242*) ClearAll[w, x, y, a, b, c, k, s]; pde = D[w[x, y], x] + (a*x*y + b*x^2 + c*x + k*y + s)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 243*) ClearAll[w, x, y, a]; pde = D[w[x, y], x] + (y^2 - a^2*x^2 + 3*a)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 244*) ClearAll[w, x, y, a]; pde = D[w[x, y], x] + (y^2 - a^2*x^2 + a)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 245*) ClearAll[w, x, y, a]; pde = D[w[x, y], x] + (y^2 + a*x*y + a)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 246*) ClearAll[w, x, y, a, b]; pde = D[w[x, y], x] + (y^2 + a*x*y - a*b*x - b^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 247*) ClearAll[w, x, y, a, b, c, k]; pde = D[w[x, y], x] + k*(a*x + a*y + c)^2*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 248*) ClearAll[w, x, y, a, c]; pde = x*D[w[x, y], x] + (a*y^2 + c*x^2 + y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 249*) ClearAll[w, x, y, a, c, b]; pde = x*D[w[x, y], x] + (a*y^2 + b*x*y + c*x^2 + y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 250*) ClearAll[w, x, y, a, c, b, alpha, gamma, beta]; pde = (a*x + c)*D[w[x, y], x] + (alpha*(a*y + b*x)^2 + beta*(a*y + b*x) - b*x + gamma)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 251*) ClearAll[w, x, y, a, b]; pde = a*x^2*D[w[x, y], x] + b*y^2*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 252*) ClearAll[w, x, y, a, b]; pde = (a*x^2 + b)*D[w[x, y], x] - (y^2 - 2*x*y + (1 - a)*x^2 - b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 253*) ClearAll[w, x, y, a1, b1, c1, a2, b2, c2]; pde = (a1*x^2 + b1*x + c1)*D[w[x, y], x] + (a2*y^2 + b2*y + c2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 254*) ClearAll[w, x, y, a, b]; pde = (x - a)*(x - b)*D[w[x, y], x] - (y^2 + k*(y + x - a)*(y + x - b))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 255*) ClearAll[w, x, y, a1, b1, c1, a2, b2, c2]; pde = (a1*y^2 + b1*y + c1)*D[w[x, y], x] + (a2*x^2 + b2*x + c2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 256*) ClearAll[w, x, y, a, b, c]; pde = y*(a*x + b)*D[w[x, y], x] + (a*y^2 - c*x)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 257*) ClearAll[w, x, y, a, b, c]; pde = (a*y^2 + b*x)*D[w[x, y], x] - (x*x^2 + b*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 258*) ClearAll[w, x, y, a, b]; pde = (a*y^2 + b*x^2)*D[w[x, y], x] + 2*b*x*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 259*) ClearAll[w, x, y, a, b]; pde = (a*y^2 + b*x^2)*D[w[x, y], x] + 2*b*x*y*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 260*) ClearAll[w, x, y, a, b]; pde = (a*y^2 + x^2)*D[w[x, y], x] + (b*x^2 + c - 2*x*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 261*) ClearAll[w, x, y, a, b, A, B, C0]; pde = (A*y^2 + B*x^2 - a^2*B)*D[w[x, y], x] + (C0*y^2 + 2*B*x*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 262*) ClearAll[w, x, y, a, b, c]; pde = (a*y^2 + b*x^2 + c*y)*D[w[x, y], x] + 2*b*x*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 263*) ClearAll[w, x, y, A, B, D0, E0, F, k]; pde = (A*x*y + B*x^2 + k*x)*D[w[x, y], x] + (D0*y^2 + E0*x*y + F*x^2 + k*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 264*) ClearAll[w, x, y, A, B, D0, E0, C0, k]; pde = (A*x*y + A*k*y + B*x^2 + B*k*x)*D[w[x, y], x] + (C0*y^2 + D0*x*y + k*(D0 - B)*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 265*) ClearAll[w, x, y, A, B, D0, E0, C0, k, F0]; pde = (A*y^2 + B*x*y + C0*x^2 + k*x)*D[w[x, y], x] + (D0*y^2 + E0*x*y + F0*x^2 + k*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 266*) ClearAll[w, x, y, A, B, D0, E0, C0, F0]; pde = (A*y^2 + B*x*y + C0*x^2)*D[w[x, y], x] + (D0*y^2 + E0*x*y + F0*x^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 267*) ClearAll[w, x, y, A, B, D0, E0, b, a]; pde = (A*y^2 + 2*B*x*y + D0*x^2 + a)*D[w[x, y], x] - (D0*y^2 + 2*D0*x*y - E0*x^2 - b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 268*) ClearAll[w, x, y, a]; pde = (y^2 - 2*x*y + x^2 + a*y)*D[w[x, y], x] + a*y*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 269*) ClearAll[w, x, y, a1, a2, a3, b1, b2, b3, c1, c2, c3]; pde = (x*(a1 + b1*x + c1*y) - (a2 + b2*x + c2*y))*D[w[x, y], x] + (y*(a1 + b1*x + c1*y) - (a3 + b3*x + c3*y))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 270*) ClearAll[w, x, y, a, b]; pde = D[w[x, y], x] + (y^2 + b*x^2*y - a^2 - a*b*x)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 271*) ClearAll[w, x, y, a, b, c]; pde = D[w[x, y], x] + (a*x^2*y + b*x^3 + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 272*) ClearAll[w, x, y, a, b]; pde = D[w[x, y], x] + (a*x^2*y + b*y^3)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 273*) ClearAll[w, x, y, a, b]; pde = D[w[x, y], x] + (a*x*y + b)*y^2*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 274*) ClearAll[w, x, y, a, b, A]; pde = D[w[x, y], x] + A*(a*x + b*y + c)^3*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 275*) ClearAll[w, x, y, a, b, c]; pde = x*D[w[x, y], x] + (a*x^4*y^3 + (b*x^2 - 1)*y + c*x)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 276*) ClearAll[w, x, y, a, b, c]; pde = x^2*D[w[x, y], x] + (a*x^2*y^2 + b*x*y + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 277*) ClearAll[w, x, y, a, b, c]; pde = (a*x^2*y + b)*D[w[x, y], x] - (a*x*y^2 + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 278*) ClearAll[w, x, y, a, b, c]; pde = (a*x + b*y^3)*D[w[x, y], x] - (c*x^3 + a*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 279*) ClearAll[w, x, y, a]; pde = D[w[x, y], x] + (a*Sqrt[x]*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 280*) ClearAll[w, x, y, a]; pde = D[w[x, y], x] + (a*Sqrt[x]*y + b*Sqrt[y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 281*) ClearAll[w, x, y, a]; pde = D[w[x, y], x] + (a*Sqrt[x]*y + b*x*Sqrt[y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 282*) ClearAll[w, x, y, a, b, c, A]; pde = D[w[x, y], x] + A*Sqrt[a*x + b*y + c]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 283*) ClearAll[w, x, y, a, b]; pde = x*D[w[x, y], x] + (a*y + b*Sqrt[y^2 + c*x^2])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 284*) ClearAll[w, x, y, a, b, c]; pde = (a*x + b*Sqrt[y])*D[w[x, y], x] - (c*Sqrt[x] + a*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 285*) ClearAll[w, x, y, t, n, a]; f[t_] := Sum[a[n]*t^n, {n, 1, 4}]; pde = Sqrt[f[x]]*D[w[x, y], x] + Sqrt[f[y]]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 286*) ClearAll[w, x, y, k]; pde = D[w[x, y], x] + (a*y + b*x^k)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 287*) ClearAll[w, x, y, n, k]; pde = D[w[x, y], x] + (a*x^k*y + b*x^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 288*) ClearAll[w, x, y, n, a, b]; pde = D[w[x, y], x] + (a*y^2 + b*x^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 289*) ClearAll[w, x, y, n, a]; pde = D[w[x, y], x] + (y^2 + a*n*x^(n - 1) - a^2*x^(2*n))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 290*) ClearAll[w, x, y, n, a]; pde = D[w[x, y], x] + (y^2 + a*x^n*y + a*x^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 291*) ClearAll[w, x, y, n, a, b]; pde = D[w[x, y], x] + (y^2 + a*x^n*y - a*b*x^n - b^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 292*) ClearAll[w, x, y, n, a, b]; pde = D[w[x, y], x] + (a*x^n*y^2 + b*x^(-n - 2))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 293*) ClearAll[w, x, y, n, a, b, m]; pde = D[w[x, y], x] + (a*x^n*y^2 + b*m*x^(m - 1) - a*b^2*x^(n + 2*m))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 294*) ClearAll[w, x, y, n, a, b, m]; pde = D[w[x, y], x] + ((n + 1)*x^n*y^2 - a*x^(n + m + 1)*y + a*x^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 295*) ClearAll[w, x, y, n, a, b, m, c]; pde = D[w[x, y], x] + (a*x^n*y^2 + b*x^m*y + b*c*x^m - a*c^2*x^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 296*) ClearAll[w, x, y, n, a, b, m, c]; pde = D[w[x, y], x] + (a*x^n*y^2 - a*x^n*(b*x^m + c)*y + b*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 297*) ClearAll[w, x, y, n, a, b, m, c]; pde = D[w[x, y], x] - (a*n*x^(n - 1)*y^2 - c*x^m*(a*x^n + b) + c*x^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 298*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = D[w[x, y], x] + (a*x^n*y^2 + b*x^m*y + c*k*x^(k - 1) - b*c*x^(m + k) - a*c^2*x^(n + 2*k))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 299*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = D[w[x, y], x] + (a*x^(2*n + 1)*y^3 + b*x^(-n - 2))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 300*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = D[w[x, y], x] + (a*x^n*y^3 + 3*a*b*x^(n + m)*y^2 - b*m*x^(m - 1) - 2*a*b^3*x^(n + 3*m))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 301*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = D[w[x, y], x] + (a*x^n*y^3 + 3*a*b*x^(n + m)*y^2 + c*x^k*y - 2*a*b^3*x^(n + 3*m) + b*c*x^(m + l) - b*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 302*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = D[w[x, y], x] + (a*y^n + b*x^(n/(1 - n)))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 303*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = D[w[x, y], x] + (a*x^(m - n - m*n)*y^n + b*x^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 304*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = D[w[x, y], x] + (a*x^n*y^k + b*x^m*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 305*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*y^2 + b*y + c*x^(2*b))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 306*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*y^2 + (n + b*x^n)*y + c*x^(2*n))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 307*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*x^n*y^2 + b*y + c/x^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 308*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*x^n*y^2 + m*y - a*b^2*x^(x + 2*m))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 309*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (x^(2*n)*y^2 + (m - n)*y + x^(2*m))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 310*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*x^(2*n)*y^2 + (b*x^n - n)*y + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 311*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*x^(2*n + m)*y^2 + (b*x^(n + m) - n)*y + c*x^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 312*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*y^3 + 3*a*b*x^n*y^2 - b*n*x^n - 2*a*b^3*x^(3*n))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 313*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*x^(2*n + 1)*y^3 + (b*x - n)*y + c*x^(1 - n))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 314*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (a*x^(n + 2)*y^3 + (b*x^n - 1)*y + c*x^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 315*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*D[w[x, y], x] + (y + a*x^(n - m)*y^m + b*x^(n - k)*y^k)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 316*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = y*D[w[x, y], x] + (x^(n - 1)*((1 + 2*n)*x + a*n)*y - n*x^(2*n)*(x + a))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 317*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = y*D[w[x, y], x] + ((a*(2*n + k)*x^k + b)*x^(n - 1)*y - (a^2*n*x^(2*k) + a*b*x^k - c)*x^(2*n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 318*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x*(2*a*x*y + b)*D[w[x, y], x] - (a*(m + 3)*x*y^2 + b*(m + 2)*y - c*x^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 319*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = x^2*(2*a*x*y + b)*D[w[x, y], x] - (4*a*x^2*y^2 + 3*b*x*y - c*x^2 - k)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 320*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = a*x^m*D[w[x, y], x] + b*y^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 321*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = a*x^n*D[w[x, y], x] + (b*y + c*x^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 322*) ClearAll[w, x, y, n, a, b, m, c, k]; pde = a*x^k*D[w[x, y], x] + (y^n + b*x^m*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}, Assumptions -> {n != 1}], 60*10]]; (*----------------------------*) (*PDE number 323*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma]; pde = x*(a*x^k + b)*D[w[x, y], x] + (alpha*x^n*y^2 + (beta - a*n*x^k)*y + gamma/x^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 324*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A]; pde = (y + A*x^n + a)*D[w[x, y], x] - (n*A*x^(n - 1)*y + k*x^m + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 325*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A]; pde = (y + a*x^(n + 1) + b*x^n)*D[w[x, y], x] + (a*n*x^n + c*x^(n - 1))*y*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 326*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0]; pde = x*(2*a*x^n*y + b)*D[w[x, y], x] - (a*(3*n + m)*x^n*y^2 + b*(2*n + m)*y - A*x^m - C0/x^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 327*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0]; pde = (a*x^n + b*x^2 + x*y)*D[w[x, y], x] + (c*x^n + b*x*y + y^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 328*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0]; pde = (a*y^n + b*x^2 + c*x*y)*D[w[x, y], x] + (k*y^n + b*x*y + c*y^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 329*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0]; pde = (a*x^n + b*x^m + c)*D[w[x, y], x] + (c*y^2 - b*x^(m - 1)*y + a*x^(n - 2))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 330*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0]; pde = (a*x^n + b*x^m + c)*D[w[x, y], x] + (a*x^(n - 2)*y^2 + b*x^(m - 1)*y + c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 331*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda]; pde = (a*x^n + b*x^m + c)*D[w[x, y], x] + (alpha*x^k*y^2 + beta*x^s*y - alpha*lambda^2*x^k + beta*lambda*x^s)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 332*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda]; pde = x*(a*x^n + b*x^m + c)*D[w[x, y], x] - (s*x^k*y^2 - (a*x^n + b*x^m + c)*y - s*lambda*x^(k + 2))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 333*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda]; pde = (a*x^n + b*x^m + c)*D[w[x, y], x] + ((a*x^n + b*x^m + c)*y^2 - a*n*(n - 1)*x^(n - 2) - b*m*(m - 1)*x^(m - 2))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 334*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda]; pde = (a*x^n + b*y^n + x)*D[w[x, y], x] + (alpha*x^k*y^(n - k) + beta*x^m*y^(n - m) + y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 335*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B]; pde = (a*x^n + b*y^n + A*x^2 + B*x*y)*D[w[x, y], x] + (alpha*x^k*y^(n - k) + beta*x^m*y^(n - m) + A*x*y + B*y^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 336*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = (a*y^m + b*x^n + s)*D[w[x, y], x] - (alpha*x^k + b*n*x^(n - 1)*y + beta)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 337*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = (a*x^n*y^m + x)*D[w[x, y], x] + (b*x^k*y^(n + m - k) + y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 338*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = x*(a*x^n*y^m + alpha)*D[w[x, y], x] - y*(b*x^n*y^m + beta)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 339*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = x*(a*n*x^k*y^(n + k) + s)*D[w[x, y], x] - y*(b*m*x^(m + k)*y^k + s)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 340*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = (a*x^n*y^m + A*x^2 + B*x*y)*D[w[x, y], x] + (b*x^k*y^(n + m - k) + A*x*y + B*y^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 341*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = (a*x^n*y^m + b*x*y^k)*D[w[x, y], x] + (alpha*y^s + beta)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 342*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = D[w[x, y], x] + a*Exp[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 343*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = D[w[x, y], x] + (a*Exp[lambda*x] + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 344*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = D[w[x, y], x] + (a*Exp[lambda*y] + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 345*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = D[w[x, y], x] + (a*Exp[lambda*y + beta*x] + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 346*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = D[w[x, y], x] + (a*Exp[lambda*y + beta*x] + b*Exp[gamma*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 347*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*Exp[beta*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 348*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = (a*Exp[lambda*x] + b)*D[w[x, y], x] + (c + Exp[beta*x] + d)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 349*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = (a*Exp[lambda*x] + b)*D[w[x, y], x] + (c + Exp[beta*y] + d)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 350*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = (a*Exp[lambda*y] + b)*D[w[x, y], x] + (c + Exp[beta*x] + d)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 351*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s]; pde = (a*Exp[lambda*x] + b*Exp[beta*y])*D[w[x, y], x] + a*lambda*Exp[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 352*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = (a*Exp[lambda*x + beta*y] + c*mu)*D[w[x, y], x] - (b*Exp[gamma*x + mu*y] + c*lambda)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 353*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (y^2 + a*lambda*Exp[lambda*x] - a^2*Exp[2*lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 354*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (y^2 + b*y + a*(lambda - b)*Exp[lambda*x] - a^2*Exp[2*lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 355*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (y^2 + a*Exp[lambda*x]*y - a*b*Exp[lambda*x] - b^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 356*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] - (y^2 - a*x*Exp[lambda*x]*y + a*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 357*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^2 + b*Exp[-(lambda*x)])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 358*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^2 + b*mu*Exp[mu*x] - a*b^2*Exp[(lambda + 2*mu)*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 359*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^2 + b*y + c*Exp[-(lambda*x)])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 360*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^2 + mu*y - a*b^2*Exp[(lambda + 2*mu)*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 361*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (Exp[lambda*x]*y^2 + a*Exp[mu*x]*y + a*lambda*Exp[(mu - lambda)*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 362*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] - (lambda*Exp[lambda*x]*y^2 - a*Exp[mu*x]*y + a*lambda*Exp[(mu - lambda)*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 363*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^2 + a*b*Exp[(lambda + mu)*x]*y - b*mu*Exp[mu*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 364*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[(2*lambda + mu)*x]*y^2 + (b*Exp[(lambda + mu)*x] - lambda)*y + c*Exp[mu*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 365*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (Exp[lambda*x]*(y - b*Exp[mu*x])^2 + b*mu*Exp[mu*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 366*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^2 + b*n*x^(n - 1) - a*b^2*Exp[lambda*x]*x^(2*n))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 367*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (Exp[lambda*x]*y^2 + a*x^n*y + a*lambda*x^n*Exp[-(lambda*x)])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 368*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (lambda*Exp[lambda*x]*y^2 + a*x^n*Exp[lambda*x]*y - a*x^n*Exp[2*lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 369*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^2 - a*b*x^n*Exp[lambda*x]*y + b*n*x^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 370*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*x^n*y^2 + b*lambda*Exp[lambda*x] - a*b^2*x^n*Exp[2*lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 371*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*x^n*y^2 + lambda*y - a*b^2*x^n*Exp[2*lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 372*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*x^n*y^2 - a*b*x^n*Exp[lambda*x]*y + b*lambda*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 373*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*x^n*y^2 - a*x^n*(b*Exp[lambda*x] + c)*y + b*lambda*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 374*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*x^n*Exp[2*lambda*x]*y^2 + (b*x^n*Exp[lambda*x] - lambda)*y + c*x^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 375*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*(y - b*x^n - c)^2 + b*n*x^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 376*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (y^2 + 2*a*lambda*x*Exp[lambda*x^2] - a^2*Exp[2*lambda*x^2])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 377*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*Exp[-(lambda*x^2)]*y^2 + lambda*x*y + a*b^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 378*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu]; pde = D[w[x, y], x] + (a*x^n*y^2 + lambda*x*y + a*b^2*x^n*Exp[lambda*x^2])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 379*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Exp[2*lambda*x]*y^3 + b*Exp[lambda*x]*y^2 + c*y + d*Exp[-(lambda*x)])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 380*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^3 + 3*a*b*Exp[lambda*x]*y^2 + c*y - 2*a*b^3*Exp[lambda*x] + b*c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 381*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (a*Exp[lambda*x]*y^2 + k*y + a*b^2*x^(2*k)*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 382*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (a*x^(2*n)*Exp[lambda*x]*y^2 + (b*x^n*Exp[lambda*x] - n)*y + c*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 383*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = y*D[w[x, y], x] + Exp[lambda*x]*((2*a*lambda*x + a + b)*y - Exp[lambda*x]*(a^2*lambda*x^2 + a*b*x - c))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 384*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*y^m*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 385*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*Exp[y] + b*x)*D[w[x, y], x] + D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 386*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n*Exp[lambda*y] + b*x*y^m)*D[w[x, y], x] + Exp[mu*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 387*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n*y^m + b*x*Exp[lambda*y])*D[w[x, y], x] + y^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 388*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n*y^m + b*x*y^k)*D[w[x, y], x] + Exp[lambda*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 389*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Sinh[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 390*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Sinh[mu*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 391*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 - a^2 + a*lambda*Sinh[lambda*x] - a^2*Sinh[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 392*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + lambda*(Sinh[lambda*x]*y^2 - Sinh[lambda*x]^3)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 393*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + ((a*Sinh[lambda*x]^2 - lambda)*y^2 - a*Sinh[lambda*x]^2 + lambda - a)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 394*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = Sinh[lambda*x]*D[w[x, y], x] + a*Sinh[mu*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 395*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = Sinh[mu*yx]*D[w[x, y], x] + a*Sinh[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 396*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Cosh[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 397*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Cosh[lambda*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 398*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + ((a*Cosh[lambda*x]^2 - lambda)*y^2 - a*Cosh[lambda*x]^2 + lambda + a)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 399*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = 2*D[w[x, y], x] + ((a - lambda + a*Cosh[lambda*x])*y^2 + a + lambda - a*Cosh[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 400*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n + b*x*Cosh[y]^m)*D[w[x, y], x] + y^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 401*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n + b*x*Cosh[y]^m)*D[w[x, y], x] + Cosh[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 402*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n*y^m + b*x)*D[w[x, y], x] + Cosh[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 403*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = Cosh[mu*y]*D[w[x, y], x] + a*Cosh[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 404*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Tanh[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 405*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Tanh[lambda*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 406*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + a*lambda - a*(a + lambda)*Tanh[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 407*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + 3*a*lambda - lambda^2 - a*(a + lambda)*Tanh[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 408*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n + b*x*Tanh[y]^m)*D[w[x, y], x] + y^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 409*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n + b*x*Tanh[y]^m)*D[w[x, y], x] + Tanh[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 410*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n*y^m + b*x)*D[w[x, y], x] + Tanh[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 411*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n*Tanh[y]^m)*D[w[x, y], x] + y^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 412*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Coth[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 413*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Coth[lambda*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 414*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + a*lambda - a*(a + lambda)*Coth[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 415*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + 3*a*lambda - lambda^2 - a*(a + lambda)*Coth[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 416*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Sinh[lambda*x]*Cosh[mu*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 417*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Cosh[lambda*x]*Sinh[mu*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 418*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 - 2*lambda^2*Tanh[lambda*x]^2 - 2*lambda^2*Coth[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 419*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + lambda*(a + b) - 2*a*b - a*(a + lambda)*Tanh[lambda*x]^2 - b*(b + lambda)*Coth[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 420*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = Sinh[lambda*y]*D[w[x, y], x] + a*Cosh[beta*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 421*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n*Cosh[lambda*y]^m + b*x)*D[w[x, y], x] + Sinh[beta*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 422*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Log[lambda*x]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 423*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Log[lambda*y]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 424*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Log[x + lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 425*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*x^n*Log[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 426*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*y^n*Log[lambda*x]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 427*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + a*Log[beta*x]*y - a*b*Log[beta*x] - b^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 428*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + a*x*Log[b*x]^m*y + a*Log[b*x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 429*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*x^n*y^2 - a*b*x^(n + 1)*y*Log[x] + b*Log[x] + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 430*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] - ((n + 1)*x^n*y^2 - a*x^(n + 1)*Log[x]^m*y + a*Log[x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 431*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Log[x]^n*y^2 + b*m*x^(m - 1) - a*b^2*x^(2*m)*Log[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 432*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Log[x]^n*y^2 - a*b*x*y*Log[x]^(n + 1) + b*Log[x] + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 433*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Log[x]^k*(y - b*x^n - c)^3 + b*n*x^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 434*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Log[x]^n*y^2 + b*Log[x]^m*y + b*c*Log[x]^m - a*c^2*Log[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 435*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (a*y + b*Log[x])^2*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 436*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (x*y^2 - A^2*x*Log[beta*x]^2 + A)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 437*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (x*y^2 - A^2*x*Log[beta*x]^(2*k) + k*A*Log[beta*x]^(k - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 438*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (a*x^n*y^2 + b - a*b^2*x^n*Log[x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 439*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (a*Log[lambda*x]^m*y^2 + k*y + a*b^2*x^(2*k)*Log[lambda*x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 440*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (a*x^n*(y + b*Log[x])^2 - b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 441*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (a*x^(2*n)*Log[x]*y^2 + (b*x^n*Log[x] - n)*y + c*Log[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 442*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x^k*D[w[x, y], x] + (a*y^n*Log[x]^m + b*y*Log[x]^s)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 443*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*Log[x] + b)*D[w[x, y], x] + (y^2 + c*Log[x]^n*y - lambda^2 + lambda*c*Log[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 444*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*Log[x] + b)*D[w[x, y], x] + (Log[x]^n*y^2 - c*y - lambda^2*Log[x]^n + c*lambda)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 445*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x^2*Log[a*x]*D[w[x, y], x] - (x^2*y^2*Log[a*x] + 1)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 446*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = Log[lambda*x]^k*D[w[x, y], x] + (a*y^n + b*y*Log[x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 447*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = Log[lambda*x]^k*D[w[x, y], x] + (a*y^n*Log[x]^m + b*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 448*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Sin[lambda*x]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 449*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Sin[lambda*y]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 450*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Sin[lambda*x]^k*Sin[mu*y]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 451*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Sin[x + lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 452*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 - a^2 + a*lambda*Sin[lambda*x] + a^2*Sin[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 453*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + a*Sin[beta*x]*y + a*b*Sin[beta*x] - b^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 454*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 + a*x*Sin[b*x]^m*y + a*Sin[b*x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 455*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (lambda*Sin[lambda*x]*y^2 + lambda*Sin[lambda*x]^3)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 456*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = 2*D[w[x, y], x] + ((lambda + a - a*Sin[lambda*x])*y^2 + lambda - a - a*Sin[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 457*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + ((lambda + a*Sin[lambda*x]^2)*y^2 + lambda - a + a*Sin[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 458*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] - ((k + 1)*x^k*y^2 - a*x^(k + 1)*Sin[x]^m*y + a*Sin[x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 459*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Sin[lambda*x + mu]^k*(y - b*x^n - c)^2 + y - b*x^n + b*n*x^(n - 1) - c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 460*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = x*D[w[x, y], x] + (a*Sin[lambda*x]^m*y^2 + k*y + a*b^2*x^(2*k)*Sin[lambda*x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 461*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*Sin[lambda*x] + b)*D[w[x, y], x] + (y^2 + c*Sin[mu*x]*y - k^2 + c*k*Sin[mu*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 462*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Cos[lambda*x]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 463*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (a*Cos[lambda*y]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 464*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Cos[lambda*y]^k*Cos[mu*y]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 465*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + a*Cos[x + lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 466*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (y^2 - a^2 + a*lambda*Cos[lambda*x] + a^2*Cos[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 467*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + (lambda*Cos[lambda*x]*y^2 + lambda*Cos[lambda*x]^3)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 468*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = 2*D[w[x, y], x] + ((lambda + a + a*Cos[lambda*x])*y^2 + lambda - a + a*Cos[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 469*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = D[w[x, y], x] + ((lambda + a*Cos[lambda*x]^2)*y^2 + lambda - a + a*Cos[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 470*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n*y^m + b*x)*D[w[x, y], x] + Cos[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 471*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d]; pde = (a*x^n + b*x*Cos[y]^m)*D[w[x, y], x] + y^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 472*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = (a*x^n + b*x*Cos[y]^m)*D[w[x, y], x] + Cos[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 473*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = (a*x^n*Cos[y]^m + b*x)*D[w[x, y], x] + Cos[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 474*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (a + Tan[lambda*x] + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 475*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (a + Tan[lambda*y] + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 476*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + a*Tan[lambda*x]^k*Tan[mu*y]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 477*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (y^2 + a*lambda + a*(lambda - a)*Tan[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 478*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (y^2 + lambda^2 + 3*a*lambda + a*(lambda - a)*Tan[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 479*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (y^2 + a*x*Tan[b*x]^k*y + a*Tan[b*x]^k)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 480*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] - ((k + 1)*x^k*y^2 - a*x^(k + 1)*Tan[x]^m*y + a*Tan[x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 481*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (a*Tan[lambda*x]^n*y^2 - a*b^2*Tan[lambda*x]^(n + 2) + b*lambda*Tan[lambda*x]^2 + b*lambda)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 482*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (a*Tan[lambda*x + mu]^k*(y - b*x^n - c)^2 + y - b*x^n + b*n*x^(n - 1) - c)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 483*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = x*D[w[x, y], x] + (a*Tan[lambda*x]^m*y^2 + k*y + a*b^2*x^(2*k)*Tan[lambda*x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 484*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = (a*Tan[lambda*x] + b)*D[w[x, y], x] + (y^2 + c*Tan[mu*x]*y - k^2 + c*k*Tan[mu*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 485*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = (a*x^n*y^m + b*x)*D[w[x, y], x] + Tan[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 486*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = (a*x^n + b*x*Tan[y]^m)*D[w[x, y], x] + y^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 487*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = (a*x^n + b*x*Tan[y]^m)*D[w[x, y], x] + Tan[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 488*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = (a*x^n*Tan[y]^m + b*x)*D[w[x, y], x] + Tan[lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 489*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (a*Cot[lambda*x]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 490*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (a*Cot[lambda*y]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 491*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + a*Cot[x + lambda*y]^k*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 492*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (y^2 + a*lambda + a*(lambda - a)*Cot[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 493*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (y^2 + lambda^2 + 3*a*lambda + a*(lambda - a)*Cot[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 494*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = D[w[x, y], x] + (y^2 - 2*a*Cot[a*x]*y + b^2 - a^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 495*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = Cot[lambda*x]*D[w[x, y], x] + a*Cot[mu*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 496*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = Cot[mu*y]*D[w[x, y], x] + a*Cot[lambda*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 497*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = Cot[mu*y]*D[w[x, y], x] + a*Cot[lambda*x]^2*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 498*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = Cot[y + a]*D[w[x, y], x] + c*Cot[x + b]^2*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 499*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B]; pde = Cot[lambda*x]*Cot[mu*y]*D[w[x, y], x] + a*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 500*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = Cot[lambda*x]*Cot[mu*y]*D[w[x, y], x] + a*Cot[v*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 501*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + a*Sin[lambda*x]^k*Cos[mu*y]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 502*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 - y*Tan[x] + a*(1 - a)*Cot[x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 503*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 - m*y*Tan[x] + b^2*Cos[x]^(2*m))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 504*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + m*y*Cot[x] + b^2*Sin[x]^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 505*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 - 2*lambda^2*Tan[lambda*x]^2 - 2*lambda^2*Cot[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 506*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*(a + b) + 2*a*b + a*(lambda - a)*Tan[lambda*x]^2 + b*(lambda - b)*Cot[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 507*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*Sin[lambda*x]*y^2 + a*Cos[lambda*x]^n*y - a*Cos[lambda*x]^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 508*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*Sin[lambda*x]*y^2 + a*Sin[lambda*x]*y - a*Tan[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 509*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*Sin[lambda*x]*y^2 + a*Sin[lambda*x]*y - a*Tan[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 510*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (A*Exp[lambda*x]*Cos[a*y] + B*Exp[mu*x]*Sin[a*y] + A*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 511*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = Sin[2*x]^(n + 1)*D[w[x, y], x] + (a*y^2*Sin[x]^(2*n) + b*Cos[x]^(2*n))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 512*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (a*ArcSin[lambda*x]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 513*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (a*ArcSin[lambda*y]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 514*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + k*Arcsin[a*x + b*y + c]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 515*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + a*Arcsin[lambda*x]^k*Arcsin[mu*y]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 516*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*Arcsin[x]^n*y - a^2 + a*lambda*Arcsin[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 517*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*x*Arcsin[x]^n*y + lambda*Arcsin[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 518*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] - ((k + 1)*x^k*y^2 - lambda*Arcsin[x]^n*(x^(k + 1)*y - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 519*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*Arcsin[x]^n*y^2 + a*y + a*b - b^2*lambda*Arcsin[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 520*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*Arcsin[x]^n*y^2 - b*lambda*x^m*ArcSin[x]^n*y + b*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 521*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcSin[x]^n*y^2 + b*m*x^(m - 1) - lambda*b^2*x^(2*m)*ArcSin[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 522*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcSin[x]^n*(y - a*x^m - b)^2 + a*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 523*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = x*D[w[x, y], x] + (lambda*ArcSin[x]^n*y^2 + k*y + lambda*b^2*x^(2*k)*ArcSin[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 524*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (a*ArcCos[lambda*x]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 525*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (a*ArcCos[lambda*y]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 526*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + k*ArcCos[a*x + b*y + c]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 527*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + a*ArcCos[lambda*x]^k*ArcCos[mu*y]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 528*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*ArcCos[x]^n*y - a^2 + a*lambda*ArcCos[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 529*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*x*ArcCos[x]^n*y + a*lambda*ArcCos[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 530*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] - ((k + 1)*x^k*y^2 - lambda*ArcCos[x]^n*(x^(k + 1)*y - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 531*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCos[x]^n*y^2 + a*y + a*b - b^2*lambda*ArcCos[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 532*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCos[x]^n*y^2 - b*lambda*x^m*ArcCos[x]^n*y + b*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 533*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCos[x]^n*y^2 + b*m*x^(m - 1) - lambda*b^2*x^(2*m)*ArcCos[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 534*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCos[x]^n*(y - a*x^m - b)^2 + a*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 535*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = x*D[w[x, y], x] + (lambda*ArcCos[x]^n*y^2 + k*y + lambda*b^2*x^(2*k)*ArcCos[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 536*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (a*ArcTan[lambda*x]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 537*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (a*ArcTan[lambda*y]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 538*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + k*ArcTan[a*x + b*y + c]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 539*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + a*ArcTan[lambda*x]^k*ArcTan[mu*y]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 540*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*ArcTan[x]^n*y - a^2 + a*lambda*ArcTan[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 541*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*x*ArcTan[x]^n*y + lambda*ArcTan[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 542*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] - ((k + 1)*x^k*y^2 - lambda*ArcTan[x]^n*(x^(k + 1)*y - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 543*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcTan[x]^n + a*y + a*b - b^2*lambda*ArcTan[x]^n*n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 544*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcTan[x]^n*y^2 - b*lambda*x^m*ArcTan[x]^n*y + b*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 545*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcTan[x]^n*y^2 + b*m*x^(m - 1) - lambda*b^2*x^(2*m)*ArcTan[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 546*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcTan[x]^n*(y - a*x^m - b)^2 + a*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 547*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = x*D[w[x, y], x] + (lambda*ArcTan[x]^n*y^2 + k*y + lambda*b^2*x^(2*k)*ArcTan[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 548*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCot[lambda*x]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 549*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCot[lambda*y]^k + b)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 550*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + k*ArcCot[a*x + b*y + c]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 551*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + a*ArcCot[lambda*x]^k*ArcCot[lambda*y]^n*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 552*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*ArcCot[x]^n*y - a^2 + a*lambda*ArcCot[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 553*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (y^2 + lambda*x*ArcCot[x]^n*y + lambda*ArcCot[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 554*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] - ((k + 1)*x^k*y^2 - lambda*ArcCot[x]^n*(x^(k + 1)*y - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 555*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCot[x]^n*y^2 + a*y + a*b - b^2*lambda*ArcCot[x]^n*n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 556*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCot[x]^n*y^2 - b*lambda*x^m*ArcCot[x]^n*y + b*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 557*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCot[x]^n*y^2 + b*m*x^(m - 1) - lambda*b^2*x^(2*m)*ArcCot[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 558*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = D[w[x, y], x] + (lambda*ArcCot[x]^n*(y - a*x^m - b)^2 + a*m*x^(m - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 559*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v]; pde = x*D[w[x, y], x] + (lambda*ArcCot[x]^n*y^2 + k*y + lambda*b^2*x^(2*k)*ArcCot[x]^n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 560*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y + g[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 561*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y + g[x]*y^k)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 562*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (y^2 + f[x]*y - a^2 - a*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 563*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (y^2 + x*f[x]*y + f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 564*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] - ((k + 1)*x^k*y^2 - x^(k + 1)*f[x]*y + f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 565*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + a*y - a*b - b^2*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 566*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*x^n*f[x]*y + a*n*x^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 567*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + a*n*x^(n - 1) - a^2*x^(2*n)*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 568*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + g[x]*y - a^2*f[x] - a*g[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 569*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + g[x]*y + a*n*x^(n - 1) - a*x^n*g[x] - a^2*x^(2*n)*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 570*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*x^n*g*x*y + a*n*x^(n - 1) + a^2*x^(2*n)*(g*x - f*x))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 571*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = x*D[w[x, y], x] + (f[x]*y^2 + n*y + a*x^(2*n)*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}, Assumptions -> a > 0], 60*10]]; (*----------------------------*) (*PDE number 572*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = x*D[w[x, y], x] + (x^(2*n)*f[x]*y^2 + (a*x^n*f[x] - n)*y + b*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 573*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y^2 + a*Exp[lambda*x]*f[x]*y + lambda*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 574*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*Exp[lambda*x]*f[x]*y + a*lambda*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 575*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + a*lambda*Exp[lambda*x] - a^2*Exp[2*lambda*x]*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 576*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + lambda*y + a*Exp[2*lambda*x]*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}, Assumptions -> a > 0], 60*10]]; (*----------------------------*) (*PDE number 577*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - (a*Exp[lambda*x] + b)*f[x]*y + a*lambda*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 578*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (Exp[lambda*x]*f[x]*y^2 + (a*f[x] - lambda)*y + b*Exp[-(lambda*x)]*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 579*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + g[x]*y + a*lambda*Exp[lambda*x] - a*Exp[lambda*x]*g[x] - a^2*Exp[2*lambda*x]*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 580*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*Exp[lambda*x]*g[x]*y + a*lambda*Exp[lambda*x] + a^2*Exp[2*lambda*x]*(g[x] - f[x]))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 581*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + 2*a*lambda*x*Exp[lambda*x^2] - a^2*f[x]*Exp[2*lambda*x^2])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 582*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 + 2*lambda*x*y + a*f[x]*Exp[2*lambda*x^2])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}, Assumptions -> a > 0], 60*10]]; (*----------------------------*) (*PDE number 583*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*Exp[lambda*y] + g[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 584*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a^2*f[x] + a*lambda*Sinh[lambda*x] - a^2*f[x]*Sinh[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 585*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*(a*f[x] + lambda)*Tanh[lambda*x]^2 + a*lambda)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 586*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*(a*f[x] + lambda)*Coth[lambda*x]^2 + a*lambda)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 587*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] - (a*y^2*Log[x] - a*x*y*(Log[x] - 1)*f[x] + f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 588*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*x*Log[x]*f[x]*y + a*Log[x] + a)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 589*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = x*D[w[x, y], x] + (f[x]*y^2 + a - a^2*Log[x]^2*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 590*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = x*D[w[x, y], x] + ((y + a*Log[x])^2*f[x] - a)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 591*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (lambda*Sin[lambda*x]*y^2 + f[x]*Cos[lambda*x]*y - f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 592*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a^2*f[x] + a*lambda*Sin[lambda*x] + a^2*f[x]*Sin[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 593*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a^2*f[x] + a*lambda*Cos[lambda*x] + a^2*f[x]*Cos[lambda*x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 594*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*(a*f[x] - lambda)*Tan[lambda*x]^2 + a*lambda)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 595*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - a*(a*f[x] - lambda)*Cot[lambda*x]^2 + a*lambda)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 596*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (f[x]*y^2 - f[x]*g[x]*y + Derivative[1][g][x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 597*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] - (Derivative[1][f][x]*y^2 - f[x]*g[x]*y + g[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 598*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (g[x]*(y - f[x])^2 + Derivative[1][f][x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 599*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + ((Derivative[1][f][x]*y^2)/g[x] - Derivative[1][g][x]/f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 600*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = f[x]^2*D[w[x, y], x] + (Derivative[1][f][x]*y^2 - g[x]*(y - f[x]))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 601*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = D[w[x, y], x] + (y^2 - Derivative[2][f][x]/f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 602*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; pde = g[x]*D[w[x, y], x] + (a*f[x]*g[x]*y^3 + (b*f[x]*g[x]^3 + Derivative[1][g][x])*y + c*f[x]*g[x]^4)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 603*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + (f[x]*y^3 + 3*f[x]*h[x]*y^2 + (g[x] + 3*f[x]*h[x]^2)*y + f[x]*h[x]^3 + g[x]*h[x] - Derivative[1][h][x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 604*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + ((Derivative[1][g][x]*y^3)/(f[x]^2*(a*g[x] + b)^3) + (Derivative[1][f][x]*y)/f[x] + f[x]*Derivative[1][g][x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 605*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + ((y - f[x])*(y - g[x])*(y - (a*f[x] + b*g[x])/(a + b))*h[x] + ((y - g[x])*Derivative[1][f][x])/(f[x] - g[x]) + ((y - f[x])*Derivative[1][g][x])/(g[x] - f[x]))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 606*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + (f[x]*y^2 + Derivative[1][g][x]*y + a*f[x]*Exp[2*g[x]])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}, Assumptions -> a > 0], 60*10]]; (*----------------------------*) (*PDE number 607*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + (Derivative[1][f][x]*y^2 + a*Exp[lambda*x]*f[x]*y + a*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 608*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = f[x]*D[w[x, y], x] + g[y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 609*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (f[x] + g[y])*D[w[x, y], x] + Derivative[1][f][x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 610*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (x^n*f[y] + x*g[y])*D[w[x, y], x] + h[y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 611*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (f[y] + a*m*x^n*y^(m - 1))*D[w[x, y], x] - (g[x] + a*n*x^(n - 1)*y^m)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 612*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (Exp[alpha*x]*f[y] + c*beta)*D[w[x, y], x] - (Exp[beta*y]*g[x] + c*alpha)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 613*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + f[a*x + b*y + c]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 614*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + f[y/x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 615*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + (f[y + a*x^n + b] - a*n*x^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 616*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*D[w[x, y], x] + y*f[x^n*y^m]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 617*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = y^(m - 1)*D[w[x, y], x] + x^(n - 1)*f[a*x^n + b*y^m]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 618*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + Exp[-(lambda*x)]*f[Exp[lambda*x]*y]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 619*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + Exp[lambda*y]*f[Exp[lambda*y]*x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 620*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + y*f[Exp[alpha*x]*y^m]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 621*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*D[w[x, y], x] + f[x^n*Exp[alpha*y]]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 622*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + Exp[lambda*x - beta*y]*f[a*Exp[lambda*x] + b*Exp[beta*y]]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 623*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + (f[y + a*Exp[lambda*x] + b] - a*lambda*Exp[lambda*x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 624*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = alpha*x*y*D[w[x, y], x] + (alpha*f[x^n*Exp[alpha*y]] - n*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 625*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = m*x*Log[y]*D[w[x, y], x] + (y*f[x^n*y^m] - n*y*Log[y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 626*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + (f[y + a*Tan[x]] - a*Tan[x]^2)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 627*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = Exp[lambda*x]*D[w[x, y], x] + f[lambda*x + Log[y]]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 628*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + Exp[lambda*y]*f[lambda*y + Log[x]]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 629*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = m*x*D[w[x, y], x] - (n*y - x*y^k*f[x]*g[x^n*y^m])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 630*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = y^n*D[w[x, y], x] - (a*x^n + g[x]*f[y^(n + 1) + a*x^(n + 1)])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 631*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (f[y/x] + x^alpha*h[y/x])*D[w[x, y], x] + (g[y/x] + y*x^(alpha - 1)*h[y/x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 632*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (f[a*x + b*y] + b*x*g[a*x + b*y])*D[w[x, y], x] + (h[a*x + b*y] - a*x*g[a*x + b*y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 633*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (f[a*x + b*y] + b*y*g[a*x + b*y])*D[w[x, y], x] + (h[a*x + b*y] - a*y*g[a*x + b*y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 634*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*(f[x^n*y^m] + m*x^k*g[x^n*y^m])*D[w[x, y], x] + y*(h[x^n*y^m] - n*x^k*g[x^n*y^m])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 635*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*(f[x^n*y^m] + m*y^k*g[x^n*y^m])*D[w[x, y], x] + y*(h[x^n*y^m] - n*y^k*g[x^n*y^m])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 636*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*(s*f[x^n*y^m] - m*g[x^k*y^s])*D[w[x, y], x] + y*(n*g[x^k*y^s] - k*f[x^n*y^m])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 637*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[f[x, y], y]*D[w[x, y], x] - D[f[x, y], x]*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 638*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*D[w[x, y], x] + (x*f[x]*g[x^n*Exp[y]] - n)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 639*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = m*D[w[x, y], x] + (m*y^k*f[x]*g[Exp[alpha*x]*y^m] - alpha*y)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 640*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (f[a*x + b*y] + b*Exp[lambda*y]*g[a*x + b*y])*D[w[x, y], x] + (h[a*x + b*y] - a*Exp[lambda*y]*g[a*x + b*y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 641*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (f[a*x + b*y] + b*Exp[lambda*x]*g[a*x + b*y])*D[w[x, y], x] + (h[a*x + b*y] - a*Exp[lambda*x]*g[a*x + b*y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 642*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*(f[x^n*Exp[alpha*y]] + alpha*y*g[x^n*Exp[alpha*y]])*D[w[x, y], x] + (h[x^n*Exp[alpha*y]] - n*y*g[x^n*Exp[alpha*y]])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 643*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (f[Exp[alpha*x]*y^m] + m*x*g[Exp[alpha*x]*y^m])*D[w[x, y], x] + y*(h[Exp[alpha*x]*y^m] - alpha*x*g[Exp[alpha*x]*y^m])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 644*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*D[w[x, y], x] + (x*y*f[x]*g[x^n*Log[y]] - n*y*Log[y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 645*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*(f[x^n*y^m] + m*g[x^n*y^m]*Log[y])*D[w[x, y], x] + y*(h[x^n*y^m] - n*g[x^n*y^m]*Log[y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 646*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*(f[x^n*y^m] + m*g[x^n*y^m]*Log[x])*D[w[x, y], x] + y*(h[x^n*y^m] - n*g[x^n*y^m]*Log[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 647*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = Cos[y]*D[w[x, y], x] + (f[x]*g[Sin[x]*Sin[y]] - Cot[x]*Sin[y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 648*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = Sin[2*x]*D[w[x, y], x] + (Sin[2*x]*Cos[y]^2*f[x]*g[Tan[x]*Tan[y]] - Sin[2*y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 649*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*D[w[x, y], x] + (x*Cos[y]^2*f[x]*g[x^(2*n)*Tan[y]] - n*Sin[2*y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 650*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + (Cos[y]^2*f[x]*g[Exp[2*x]*Tan[y]] - Sin[2*y])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 651*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 652*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*Exp[x]*D[w[x, y], x] + b*D[w[x, y], y] == c*Exp[2*x]*y; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 653*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = D[w[x, y], x] + a*D[w[x, y], y] == b; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 654*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 655*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == alpha*x + beta*y + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 656*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x*D[w[x, y], x] + b*D[w[x, y], y] == alpha*x + beta*y + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 657*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x*D[w[x, y], x] + b*x*D[w[x, y], y] == c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 658*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (a*x + b)*D[w[x, y], x] + (c*y + d)*D[w[x, y], y] == alpha*x + beta*y + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 659*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*y*D[w[x, y], x] + b*D[w[x, y], y] == alpha*x + beta*y + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 660*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 661*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == c*x + k*y; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 662*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 663*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 664*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == c*x*y + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 665*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x^2*D[w[x, y], x] + b*y^2*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n*x + m*y + s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 666*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x^2*D[w[x, y], x] + a*x*y*D[w[x, y], y] == b*y^2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 667*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*y^2*D[w[x, y], x] + b*x^2*D[w[x, y], y] == c*x^2 + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 668*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*y^2*D[w[x, y], x] + b*x*y*D[w[x, y], y] == c*x^2 + d*y^2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 669*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*Sqrt[x^2 + y^2]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 670*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*x*y^2 + d*x^2*y + k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 671*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == c*x*y^2 + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 672*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = (a*x + b)*D[w[x, y], x] + (c*y + d)*D[w[x, y], y] == k*x^3 + n*y^3; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 673*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x^2*D[w[x, y], x] + x*y*D[w[x, y], y] == y^2*(a*x + b*y); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 674*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x^3*D[w[x, y], x] + b*y^3*D[w[x, y], y] == c*x + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 675*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^n + d*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 676*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^n*y; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 677*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*(x^2 + y^2)^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 678*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*x^n*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 679*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*x^n + d*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 680*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = m*x*D[w[x, y], x] + n*y*D[w[x, y], y] == (a*x^n + b*y^m)^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 681*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x^n*D[w[x, y], x] + b*y^m*D[w[x, y], y] == c*x^k + d*y^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 682*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h]; pde = a*x^n*D[w[x, y], x] + b*x^m*y*D[w[x, y], y] == c*x^k*y^s + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 683*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*x^n*D[w[x, y], x] + (b*x^m*y + c*x^k)*D[w[x, y], y] == s*x^p*y^q + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 684*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*x^n*D[w[x, y], x] + (b*x^m*y^k + c*x^l*y)*D[w[x, y], y] == s*x^p*y^q + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 685*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*y^k*D[w[x, y], x] + b*x^m*D[w[x, y], y] == c*x^m + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 686*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Exp[lambda*x] + d*Exp[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 687*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Exp[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 688*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*Exp[beta*y]*D[w[x, y], y] == c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 689*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*Exp[lambda*y]*D[w[x, y], x] + b*Exp[beta*x]*D[w[x, y], y] == c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 690*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*Exp[alpha*x]*D[w[x, y], x] + b*Exp[beta*y]*D[w[x, y], y] == c*Exp[gamma*x - beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 691*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*Exp[alpha*x]*D[w[x, y], x] + b*Exp[beta*y]*D[w[x, y], y] == c*Exp[gamma*x - 2*beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 692*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p]; pde = a*Exp[alpha*x]*D[w[x, y], x] + b*Exp[beta*y]*D[w[x, y], y] == c*Exp[gamma*x] + s*Exp[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 693*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*Exp[beta*x]*D[w[x, y], x] + (b*Exp[gamma*x] + c*Exp[lambda*y])*D[w[x, y], y] == s*Exp[mu*x] + k*Exp[delta*y] + p; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 694*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*Exp[beta*x]*D[w[x, y], x] + (b*Exp[gamma*x] + c*Exp[lambda*y])*D[w[x, y], y] == s*Exp[mu*x + delta*y] + k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 695*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*Exp[beta*x]*D[w[x, y], x] + b*Exp[gamma*x + lambda*y]*D[w[x, y], y] == c*Exp[mu*x + delta*y] + k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 696*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*Exp[lambda*y]*D[w[x, y], x] + b*Exp[beta*x]*D[w[x, y], y] == c*Exp[gamma*y] + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 697*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*y*Exp[lambda*x] + k*x*Exp[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 698*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + a*D[w[x, y], y] == a*x^k*Exp[lambda*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 699*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + (a*y + b*Exp[lambda*x])*D[w[x, y], y] == c*Exp[beta*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 700*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + (a*y*Exp[lambda*x] + b*Exp[beta*x]*y^k)*D[w[x, y], y] == c*Exp[mu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 701*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + (a*x^k + b*x^n*Exp[lambda*y])*D[w[x, y], y] == c*Exp[beta*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 702*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Exp[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 703*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*y*Exp[lambda*x] + b*x*Exp[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 704*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*x^k*D[w[x, y], x] + b*Exp[lambda*y]*D[w[x, y], y] == c*x^n + s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 705*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*y^k*D[w[x, y], x] + b*Exp[lambda*x]*D[w[x, y], y] == c*Exp[mu*x] + s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 706*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*y^k*D[w[x, y], y] == c*x^n + s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 707*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*Exp[lambda*y]*D[w[x, y], x] + b*x^k*D[w[x, y], y] == c*Exp[mu*x] + s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 708*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Sinh[lambda*x] + k*Sinh[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 709*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Sinh[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 710*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x*Sinh[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 711*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Sinh[lambda*x]*D[w[x, y], y] == c*Sinh[mu*x]^m + s*Sinh[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 712*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Sinh[lambda*y]*D[w[x, y], y] == c*Sinh[mu*x]^m + s*Sinh[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 713*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cosh[lambda*x] + k*Cosh[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 714*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cosh[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 715*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == a*x*Cosh[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 716*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Cosh[lambda*x]^n*D[w[x, y], y] == c*Cosh[mu*x]^m + s*Cosh[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 717*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Cosh[lambda*y]^n*D[w[x, y], y] == c*Cosh[mu*x]^m + s*Cosh[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 718*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Tanh[lambda*x] + k*Tanh[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 719*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Tanh[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 720*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Tanh[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 721*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Tanh[lambda*x]^n*D[w[x, y], y] == c*Tanh[mu*x]^m + s*Tanh[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 722*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Tanh[lambda*y]^n*D[w[x, y], y] == c*Tanh[mu*x]^m + s*Tanh[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 723*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Coth[lambda*x] + k*Coth[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 724*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Coth[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 725*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Coth[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 726*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Coth[lambda*x]^n*D[w[x, y], y] == c*Coth[mu*x]^m + s*Coth[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 727*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Coth[lambda*y]^n*D[w[x, y], y] == c*Coth[mu*x]^m + s*Coth[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 728*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Sinh[lambda*x] + k*Cosh[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 729*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == Tanh[lambda*x] + k*Coth[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 730*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == Sinh[lambda*x] + k*Tanh[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 731*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Cosh[mu*y]*D[w[x, y], y] == Sinh[lambda*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 732*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Sinh[mu*y]*D[w[x, y], y] == Cosh[lambda*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 733*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Log[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 734*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Log[lambda*x] + k*Log[beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 735*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Log[lambda*x]*Log[beta*y]*D[w[x, y], y] == c*Log[gamma*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 736*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Log[lambda*x]^n*D[w[x, y], y] == c*Log[mu*x]^m + s*Log[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 737*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Log[lambda*y]^n*D[w[x, y], y] == c*Log[mu*x]^m + s*Log[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 738*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*Log[lambda*x]^n*D[w[x, y], x] + b*Log[lambda*y]^k*D[w[x, y], y] == c*Log[gamma*x]^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 739*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^n + s*Log[lambda*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 740*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + a*D[w[x, y], y] == b*y^2 + c*x^n*y + s*Log[lambda*x]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 741*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + a*D[w[x, y], y] == b*Log[lambda*x]^k*Log[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 742*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + (a*y + b*x^n)*D[w[x, y], y] == c*Log[lambda*x]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 743*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == x^k*(n*Log[x] + m*Log[y]); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 744*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*x^k*D[w[x, y], x] + b*y^n*D[w[x, y], y] == c*Log[lambda*x]^m + s*Log[beta*y]^l; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 745*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Sin[lambda*x] + k*Sin[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 746*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Sin[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 747*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Sin[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 748*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Sin[lambda*x]^n*D[w[x, y], y] == c*Sin[mu*x]^m + s*Sin[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 749*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Sin[lambda*y]^n*D[w[x, y], y] == c*Sin[mu*x]^m + s*Sin[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 750*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cos[lambda*x] + k*Cos[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 751*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cos[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 752*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Cos[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 753*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Cos[lambda*x]^n*D[w[x, y], y] == c*Cos[mu*x]^m + s*Cos[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 754*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Cos[lambda*y]^n*D[w[x, y], y] == c*Cos[mu*x]^m + s*Cos[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 755*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Tan[lambda*x] + k*Tan[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 756*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Tan[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 757*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Tan[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 758*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Tan[lambda*x]^n*D[w[x, y], y] == c*Tan[mu*x]^m + s*Tan[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 759*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Tan[lambda*y]^n*D[w[x, y], y] == c*Tan[mu*x]^m + s*Tan[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 760*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cot[lambda*x] + k*Cot[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 761*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cot[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 762*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Cot[lambda*x + mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 763*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Cot[lambda*x]^n*D[w[x, y], y] == c*Cot[mu*x]^m + s*Cot[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 764*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Cot[lambda*y]^n*D[w[x, y], y] == c*Cot[mu*x]^m + s*Cot[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 765*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == Sin[lambda*x] + c*Cos[mu*y] + k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 766*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == Tan[lambda*x] + c*Sin[mu*y] + k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 767*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == Sin[lambda*x]*Cos[mu*y] + c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 768*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Sin[mu*y]*D[w[x, y], y] == Cos[lambda*x] + c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 769*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Tan[mu*y]*D[w[x, y], y] == Sin[lambda*x] + c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 770*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*Tan[mu*y]*D[w[x, y], y] == Cot[lambda*x] + c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 771*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcSin[x/lambda] + k*ArcSin[y/beta]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 772*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcSin[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 773*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*ArcSin[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 774*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*ArcSin[lambda*x]^n*D[w[x, y], y] == a*ArcSin[mu*x]^m + ArcSin[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 775*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*ArcSin[lambda*y]^n*D[w[x, y], y] == a*ArcSin[mu*x]^m + ArcSin[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 776*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcCos[x/lambda] + k*ArcCos[y/beta]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 777*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcCos[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 778*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*ArcCos[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 779*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*ArcCos[lambda*x]^n*D[w[x, y], y] == a*ArcCos[mu*x]^m + ArcCos[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 780*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*ArcCos[lambda*y]^n*D[w[x, y], y] == a*ArcCos[mu*x]^m + ArcCos[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 781*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcTan[x/lambda] + k*ArcTan[y/beta]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 782*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcTan[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 783*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*ArcTan[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 784*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*ArcTan[lambda*x]^n*D[w[x, y], y] == a*ArcTan[mu*x]^m + ArcTan[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 785*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*ArcTan[lambda*y]^n*D[w[x, y], y] == a*ArcTan[mu*x]^m + ArcTan[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 786*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcCot[x/lambda] + k*ArcCot[y/beta]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 787*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcCot[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 788*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*ArcCot[lambda*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 789*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*ArcCot[lambda*x]^n*D[w[x, y], y] == a*ArcCot[mu*x]^m + ArcCot[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 790*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*ArcCot[lambda*y]^n*D[w[x, y], y] == a*ArcCot[mu*x]^m + ArcCot[beta*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 791*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 792*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + a*D[w[x, y], y] == y*f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 793*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + a*D[w[x, y], y] == y^2*f[x] + y*g[x] + h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 794*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + a*D[w[x, y], y] == y^k*f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 795*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + a*D[w[x, y], y] == Exp[lambda*y]*f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 796*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + (a*y + f[x])*D[w[x, y], y] == g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 797*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + (a*y + f[x])*D[w[x, y], y] == y^k*g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 798*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = f[x]*D[w[x, y], x] + y^k*D[w[x, y], y] == g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 799*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = f[x]*D[w[x, y], x] + (y + a)*D[w[x, y], y] == b*y + c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 800*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = f[x]*D[w[x, y], x] + (y + a*x)*D[w[x, y], y] == g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 801*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0]; pde = f[x]*D[w[x, y], x] + (y*g1[x] + g0[x])*D[w[x, y], y] == y^2*h2[x] + y*h1[x] + h0[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 802*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0]; pde = f[x]*D[w[x, y], x] + (y*g1[x] + y^k*g2[x])*D[w[x, y], y] == h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 803*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0]; pde = f[x]*D[w[x, y], x] + (g1[x] + Exp[lambda*y])*D[w[x, y], y] == h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 804*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0]; pde = y^k*f[x]*D[w[x, y], x] + g[x]*D[w[x, y], y] == h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 805*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0]; pde = y^k*f[x]*D[w[x, y], x] + (y^(k + 1)*g1[x] + g0[x])*D[w[x, y], y] == y^(3*k + 1)*h2[x] + y^(2*k + 1)*h1[x] + y^k*h0[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 806*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0]; pde = f[x]*Exp[lambda*x]*D[w[x, y], x] + g[x]*D[w[x, y], y] == h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 807*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == f[x] + g[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 808*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + a*D[w[x, y], y] == f[x]*g[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 809*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; pde = D[w[x, y], x] + (a*y + f[x])*D[w[x, y], y] == g[x]*h[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 810*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0]; pde = f[x]*D[w[x, y], x] + g[y]*D[w[x, y], y] == h1[x] + h2[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 811*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f1[x]*D[w[x, y], x] + (y*f2[x] + y^k*f3[x])*D[w[x, y], y] == g[x]*h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 812*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f1[x]*g1[x]*D[w[x, y], x] + f2[x]*g2[x]*D[w[x, y], y] == h1[x]*h2[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 813*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f1[x]*g1[y]*D[w[x, y], x] + f2[x]*g2[y]*D[w[x, y], y] == h1[x] + h2[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 814*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == f[alpha*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 815*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == x*f[y/x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 816*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == f[x^2 + y^2]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 817*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == x*f[y/x] + g[x^2 + y^2]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 818*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == x^k*f[x^n*x^m]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 819*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = m*x*D[w[x, y], x] + n*y*D[w[x, y], y] == f[a*x^n + b*x^m]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 820*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x^2*D[w[x, y], x] + x*y*D[w[x, y], y] == y^k*f[alpha*x + beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 821*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (f[x]*D[w[x, y], x])/Derivative[1][f][x] + (g[y]*D[w[x, y], y])/Derivative[1][g][y] == h[f[x] + g[y]]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 822*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == f[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 823*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == f[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 824*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + g[x]*y*D[w[x, y], y] == h[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 825*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x]*y + g0[x])*D[w[x, y], y] == h[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 826*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x]*y + g0[x]*y^k)*D[w[x, y], y] == h[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 827*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x] + g0[x]*Exp[lambda*y])*D[w[x, y], y] == h[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 828*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f1[x]*g1[y]*D[w[x, y], x] + f2[x]*g2[y]*D[w[x, y], y] == h[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 829*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*y*D[w[x, y], y] == b*y^2*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 830*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*y*D[w[x, y], y] == b*Exp[lambda*x]*y*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 831*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == b*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 832*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 833*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + y*D[w[x, y], y] == b*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 834*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 835*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*(D[w[x, y], x] - b*D[w[x, y], y]) == c*y*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 836*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 837*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (x - a)*D[w[x, y], x] + (y - b)*D[w[x, y], y] == w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 838*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (y + a*x)*D[w[x, y], x] + (y - a*x)*D[w[x, y], y] == b*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 839*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (x^2 - y^2)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 840*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x^2*D[w[x, y], x] + a*x*y*D[w[x, y], y] == b*y^2*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 841*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x^2*D[w[x, y], x] + b*y^2*D[w[x, y], y] == (x + c*y)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 842*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x^2*D[w[x, y], x] + a*y^2*D[w[x, y], y] == (b*x^2 + c*x*y + d*y^2)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 843*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = y^2*D[w[x, y], x] + a*x^2*D[w[x, y], y] == (b*x^2 + c*y^2)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 844*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*y*D[w[x, y], x] + a*y^2*D[w[x, y], y] == (b*x + c*y + d)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 845*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*(a*y + b)*D[w[x, y], x] + (a*y^2 - b*x)*D[w[x, y], y] == a*y*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 846*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*(k*y - x + a)*D[w[x, y], x] - y*(k*x - y + a)*D[w[x, y], y] == b*(y - x)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 847*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*x^3 + d*y^3)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 848*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*Sqrt[x^2 + y^2]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 849*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x^2*D[w[x, y], x] + x*y*D[w[x, y], y] == y^2*(a*x + b*y)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 850*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x^2*y*D[w[x, y], x] + a*x*y^2*D[w[x, y], y] == (b*x*y + c*x + d*y + k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 851*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x*y^2*D[w[x, y], x] + b*x^2*y*D[w[x, y], y] == (a*n*y^2 + b*m*x^2)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 852*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x^3*D[w[x, y], x] + a*y^3*D[w[x, y], y] == x^2*(b*x + c*y)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 853*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*x^n + d*y^m)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 854*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^n*y*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Assuming[{n != -1, n != -2}, Simplify[sol[[2]]]]; (*----------------------------*) (*PDE number 855*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^n*y*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}, Assumptions -> n == -1], 60*10]]; (*----------------------------*) (*PDE number 856*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^n*y*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}, Assumptions -> n == -2], 60*10]]; (*----------------------------*) (*PDE number 857*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*(x^2 + y^2)^k*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 858*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*x^n*y^m*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 859*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == (c*x^n + k*y^m)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 860*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = m*x*D[w[x, y], x] + n*y*D[w[x, y], y] == (a*x^n + b*y^m)^k*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 861*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x^n*D[w[x, y], x] + b*y^m*D[w[x, y], y] == (c*x^k + d*y^s)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 862*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x^n*D[w[x, y], x] + b*x^m*y*D[w[x, y], y] == (c*x^k*y^s + d)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 863*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x^n*D[w[x, y], x] + (b*x^m*y + c*x^k)*D[w[x, y], y] == (s*x^p*y^q + d)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 864*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x^n*D[w[x, y], x] + b*x^m*y^k*D[w[x, y], y] == (c*x^p*y^q + s)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 865*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*y^k*D[w[x, y], x] + b*x^n*D[w[x, y], y] == (c*x^m + s)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol[[2]] = Simplify[sol[[2]]]; (*----------------------------*) (*PDE number 866*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*(x^n + (a*n - 1)*y^n)*D[w[x, y], x] + y*(y^n + (a*n - 1)*x^n)*D[w[x, y], y] == k*n*(x^n + y^n)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 867*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*((n - 2)*y^n - 2*x^n)*D[w[x, y], x] + y*(2*y^n - (n - 2)*x^n)*D[w[x, y], y] == ((a*(n - 2) + 2*b)*y^n - (2*a + b*(n - 2))*x^n)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 868*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Exp[alpha*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 869*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Exp[lambda*x] + k*Exp[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 870*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*Exp[beta*y]*D[w[x, y], y] == c*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 871*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[lambda*y]*D[w[x, y], x] + b*Exp[beta*x]*D[w[x, y], y] == c*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 872*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*Exp[beta*x]*D[w[x, y], y] == c*Exp[gamma*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 873*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*Exp[beta*y]*D[w[x, y], y] == (c*Exp[gamma*y] + s*Exp[delta*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 874*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[beta*x]*D[w[x, y], x] + (b*Exp[gamma*x] + c*Exp[lambda*y])*D[w[x, y], y] == (s*Exp[mu*x] + k*Exp[delta*y] + p)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 875*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[beta*x]*D[w[x, y], x] + (b*Exp[gamma*x] + c*Exp[lambda*y])*D[w[x, y], y] == (s*Exp[mu*x + delta*y] + k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 876*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[beta*x]*D[w[x, y], x] + (b*Exp[gamma*x + lambda*y])*D[w[x, y], y] == (c*Exp[mu*x + delta*y] + k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 877*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*Exp[beta*x]*D[w[x, y], y] == (c*Exp[mu*x] + k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 878*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*y*Exp[lambda*x] + k*x*Exp[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 879*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Exp[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 880*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == (a*y*Exp[lambda*x] + b*x*Exp[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 881*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x^k*D[w[x, y], x] + b*Exp[lambda*y]*D[w[x, y], y] == (c*x^n + s)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 882*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*y^k*D[w[x, y], x] + b*Exp[lambda*x]*D[w[x, y], y] == (c*Exp[mu*x] + s)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 883*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*y^k*D[w[x, y], y] == (c*x^n + s)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 884*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Exp[lambda*y]*D[w[x, y], x] + b*x^k*D[w[x, y], y] == (c*Exp[mu*x] + s)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 885*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Sinh[lambda*x] + k*Sinh[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 886*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Sinh[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 887*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Sinh[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 888*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Sinh[lambda*x]^n*D[w[x, y], y] == (c*Sinh[mu*x]^m + s*Sinh[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 889*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Sinh[lambda*y]^n*D[w[x, y], y] == (c*Sinh[mu*x]^m + s*Sinh[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 890*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Cosh[lambda*x] + k*Cosh[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 891*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cosh[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 892*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Cosh[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 893*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Cosh[lambda*x]^n*D[w[x, y], y] == (c*Cosh[mu*x]^m + s*Cosh[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 894*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Cosh[lambda*y]^n*D[w[x, y], y] == (c*Cosh[mu*x]^m + s*Cosh[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 895*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Tanh[lambda*x] + k*Tanh[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 896*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Tanh[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 897*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Tanh[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 898*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Tanh[lambda*x]^n*D[w[x, y], y] == (c*Tanh[mu*x]^m + s*Tanh[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 899*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Tanh[lambda*y]^n*D[w[x, y], y] == (c*Tanh[mu*x]^m + s*Tanh[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 900*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Coth[lambda*x] + k*Coth[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 901*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Coth[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 902*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Coth[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 903*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Coth[lambda*x]^n*D[w[x, y], y] == (c*Coth[mu*x]^m + s*Coth[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 904*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Coth[lambda*y]^n*D[w[x, y], y] == (c*Coth[mu*x]^m + s*Coth[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 905*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Sinh[lambda*x] + k*Cosh[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 906*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (Tanh[lambda*x] + k*Coth[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 907*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*Sinh[mu*y]*D[w[x, y], y] == b*Cosh[lambda*x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 908*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*Sinh[mu*y]*D[w[x, y], y] == b*Tanh[lambda*x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 909*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Sinh[lambda*x]*D[w[x, y], x] + b*Cosh[mu*y]*D[w[x, y], y] == w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 910*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Tanh[lambda*x]*D[w[x, y], x] + b*Coth[mu*y]*D[w[x, y], y] == w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 911*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Log[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 912*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Log[lambda*x] + k*Log[beta*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 913*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Log[lambda*x]^n*D[w[x, y], y] == (c*Log[lambda*x]^m + s*Log[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 914*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Log[lambda*y]^n*D[w[x, y], y] == (c*Log[lambda*x]^m + s*Log[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 915*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = Log[beta*y]*D[w[x, y], x] + a*Log[lambda*x]*D[w[x, y], y] == b*w[x, y]*Log[beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 916*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*Log[lambda*x]^n*D[w[x, y], x] + b*Log[beta*y]^k*D[w[x, y], y] == c*Log[gamma*x]^m*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 917*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*x^n + s*Log[gamma*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 918*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == (b*y^2 + c*x^n*y + s*Log[lambda*x]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 919*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == b*Log[lambda*x]^k*Log[beta*y]^n*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 920*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + (a*y + b*x^n)*D[w[x, y], y] == c*Log[lambda*x]^k*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 921*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, s, mu, d, g, B, v, f, h, q, p, delta]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == x^k*(n*Log[x] + m*Log[y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 922*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x^k*D[w[x, y], x] + b*y^n*D[w[x, y], y] == (c*Log[lambda*x]^m + s*Log[beta*y]^t)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 923*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Sin[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 924*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Sin[lambda*x] + k*Sin[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 925*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Sin[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 926*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Sin[lambda*x]^n*D[w[x, y], y] == (c*Sin[mu*x]^m + s*Sin[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 927*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Sin[lambda*y]^n*D[w[x, y], y] == (c*Sin[mu*x]^m + s*Sin[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 928*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cos[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 929*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Cos[lambda*x] + k*Cos[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 930*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Cos[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 931*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Cos[lambda*x]^n*D[w[x, y], y] == (c*Cos[mu*x]^m + s*Cos[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 932*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Cos[lambda*y]^n*D[w[x, y], y] == (c*Cos[mu*x]^m + s*Cos[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 933*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Tan[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 934*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Tan[lambda*x] + k*Tan[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 935*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Tan[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 936*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Tan[lambda*x]^n*D[w[x, y], y] == (c*Tan[mu*x]^m + s*Tan[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 937*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Tan[lambda*y]^n*D[w[x, y], y] == (c*Tan[mu*x]^m + s*Tan[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 938*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cot[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 939*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Cot[lambda*x] + k*Cot[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 940*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Cot[lambda*x + mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 941*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Cot[lambda*x]^n*D[w[x, y], y] == (c*Cot[mu*x]^m + s*Cot[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 942*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*Cot[lambda*y]^n*D[w[x, y], y] == (c*Cot[mu*x]^m + s*Cot[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 943*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == (b*Sin[lambda*x] + k*Cos[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 944*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == (b*Sin[lambda*x] + k*Tan[mu*y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 945*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*Sin[mu*y]*D[w[x, y], y] == b*Tan[lambda*x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 946*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*Tan[mu*y]*D[w[x, y], y] == b*Sin[lambda*x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 947*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = Sin[lambda*x]*D[w[x, y], x] + a*D[w[x, y], y] == b*Cos[mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 948*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = Cot[lambda*x]*D[w[x, y], x] + a*D[w[x, y], y] == b*Tan[mu*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 949*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*ArcSin[x/lambda] + k*ArcSin[y/beta])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 950*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcSin[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 951*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == a*x*ArcSin[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 952*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*ArcSin[lambda*x]^n*D[w[x, y], y] == (c*ArcSin[mu*x]^m + s*ArcSin[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 953*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*ArcSin[lambda*y]^n*D[w[x, y], y] == (c*ArcSin[mu*x]^m + s*ArcSin[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 954*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*ArcCos[x/lambda] + k*ArcCos[y/beta])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 955*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcCos[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 956*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == a*x*ArcCos[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 957*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*ArcCos[lambda*x]^n*D[w[x, y], y] == (c*ArcCos[mu*x]^m + s*ArcCos[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 958*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*ArcCos[lambda*y]^n*D[w[x, y], y] == (c*ArcCos[mu*x]^m + s*ArcCos[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 959*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*ArcTan[x/lambda] + k*ArcTan[y/beta])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 960*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcTan[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 961*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == a*x*ArcTan[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 962*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*ArcTan[lambda*x]^n*D[w[x, y], y] == (c*ArcTan[mu*x]^m + s*ArcTan[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 963*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*ArcTan[lambda*y]^n*D[w[x, y], y] == (c*ArcTan[mu*x]^m + s*ArcTan[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 964*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*ArcCot[x/lambda] + k*ArcCot[y/beta])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 965*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*ArcCot[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 966*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == a*x*ArcCot[lambda*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 967*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*ArcCot[lambda*x]^n*D[w[x, y], y] == (c*ArcCot[mu*x]^m + s*ArcCot[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 968*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*ArcCot[lambda*y]^n*D[w[x, y], y] == (c*ArcCot[mu*x]^m + s*ArcCot[beta*y]^k)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 969*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == f[x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 970*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == f[x]*y*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 971*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == (f[x]*y^2 + g[x]*y + h[x])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 972*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == f[x]*y^k*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 973*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == f[x]*Exp[lambda*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 974*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + (a*y + f[x])*D[w[x, y], y] == g[x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 975*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + (a*y + f[x])*D[w[x, y], y] == g[x]*y^k*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 976*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + y^k*D[w[x, y], y] == g[x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 977*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (y + a)*D[w[x, y], y] == (b*y + c)*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 978*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (y + a*x)*D[w[x, y], y] == g[x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 979*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x]*y + g0[x])*D[w[x, y], y] == (h2[x]*y^2 + h1[x]*y + h0[x])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 980*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x]*y + g2[x]*y^k)*D[w[x, y], y] == h[x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 981*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x]*y + g2[x]*Exp[lambda*y])*D[w[x, y], y] == h[x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 982*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*y^k*D[w[x, y], x] + g[x]*D[w[x, y], y] == h[x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 983*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*Exp[lambda*y]*D[w[x, y], x] + g[x]*D[w[x, y], y] == h[x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 984*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (f[x] + g[y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 985*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == f[x]*g[y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 986*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + (a*y + f[x])*D[w[x, y], y] == g[x]*h[y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 987*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + g[y]*D[w[x, y], y] == (h1[x] + h2[y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 988*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f1[x]*D[w[x, y], x] + (f2[x] + f3[x]*y^k)*D[w[x, y], y] == g[x]*h[y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 989*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f1[x]*g1[y]*D[w[x, y], x] + f2[x]*g2[y]*D[w[x, y], y] == h1[x]*h2[y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 990*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f1[x]*g1[y]*D[w[x, y], x] + f2[x]*g2[y]*D[w[x, y], y] == (h1[x] + h2[y])*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 991*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == f[alpha*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 992*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == x*f[y/x]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 993*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == f[x^2 + y^2]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 994*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == x^k*f[x^n*y^m]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 995*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = m*x*D[w[x, y], x] + n*y*D[w[x, y], y] == f[a*x^n + b*y^m]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 996*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = x^2*D[w[x, y], x] + x*y*D[w[x, y], y] == y^k*f[alpha*x + beta*y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 997*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (f[x]*D[w[x, y], x])/Derivative[1][f][x] + (g[x]*D[w[x, y], y])/Derivative[1][g][x] == h[f[x] + g[y]]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 998*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = D[w[x, y], x] + a*D[w[x, y], y] == f[x, y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 999*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == f[x, y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1000*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + g[x]*y*D[w[x, y], y] == h[x, y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1001*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x]*y + g0[x])*D[w[x, y], y] == h[x, y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1002*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x]*y + g0[x]*y^k)*D[w[x, y], y] == h[x, y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1003*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f[x]*D[w[x, y], x] + (g1[x]*y + g0[x]*Exp[lambda*y])*D[w[x, y], y] == h[x, y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1004*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = f1[x]*g1[y]*D[w[x, y], x] + f2[x]*g2[y]*D[w[x, y], y] == h[x, y]*w[x, y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1005*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x, y] + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1006*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (x - a)*D[w[x, y], x] + (y - b)*D[w[x, y], y] == w[x, y] - c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1007*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (a*x + b)*D[w[x, y], x] + (c*x + d)*D[w[x, y], y] == alpha*w[x, y] + beta; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1008*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (a*x + b)*D[w[x, y], x] + (c*y + d)*D[w[x, y], y] == alpha*w[x, y] + beta; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1009*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (a*x + b)*D[w[x, y], x] + (c*y + d)*D[w[x, y], y] == alpha*w[x, y] + beta*y + gamma*x; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1010*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; pde = (a*x + b)*D[w[x, y], x] + (c*x + d*y)*D[w[x, y], y] == alpha*w[x, y] + beta; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1011*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2]; pde = (a1*x + a0)*D[w[x, y], x] + (b2*y + b1*x + b0)*D[w[x, y], y] == (c2*y + c1*x + c0)*w[x, y] + k2*y + k1*x + k0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1012*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0]; pde = a*y*D[w[x, y], x] + (b1*x + b0)*D[w[x, y], y] == (c1*x + c0)*w[x, y] + s1*x + s0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1013*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x, y] + beta*x*y + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1014*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x, y] + x*(beta*x + gamma*y) + delta; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1015*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == w[x, y] + a*x^2 + b*y^2 + c; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1016*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*w[x, y] + x*(beta*x + gamma*y) + delta; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1017*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0]; pde = a*y*D[w[x, y], x] + (b2*x^2 + b1*x + b0)*D[w[x, y], y] == (c2*x^2 + c1*x + c0)*w[x, y] + s2*x^2 + s1*x + s0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1018*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0]; pde = a*y^2*D[w[x, y], x] + (b1*x^2 + b0)*D[w[x, y], y] == (c1*x^2 + c0)*w[x, y] + s1*x^2 + s0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1019*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12]; pde = (a1*x^2 + a0)*y^2*D[w[x, y], x] + (y + b2*x^2 + b1*x + b0)*D[w[x, y], y] == (c2*y + c1*x + c0)*w[x, y] + k22*y^2 + k12*x*y + k11*x^2 + k0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1020*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = (a1*x^2 + a0)*y^2*D[w[x, y], x] + (b2*y^2 + b1*x^2)*D[w[x, y], y] == (c2*y^2 + c1*x^2)*w[x, y] + s22*y^2 + s12*x*y + s11*x^2 + s0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1021*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == alpha*y*w[x, y] + beta*Sqrt[x*y] + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1022*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == lambda*Sqrt[x*y]*w[x, y] + beta*x*y + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1023*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == alpha*w[x, y] + beta*Sqrt[x] + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1024*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == alpha*w[x, y] + beta*Sqrt[x] + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1025*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*Sqrt[x]*D[w[x, y], x] + b*Sqrt[y]*D[w[x, y], y] == alpha*w[x, y] + beta*x + gamma*y + delta; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1026*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*Sqrt[x]*D[w[x, y], x] + b*Sqrt[y]*D[w[x, y], y] == alpha*w[x, y] + beta*Sqrt[x] + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1027*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*Sqrt[y]*D[w[x, y], x] + b*Sqrt[x]*D[w[x, y], y] == alpha*w[x, y] + beta*Sqrt[x] + gamma; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1028*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x, y] + k*x^n*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1029*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*D[w[x, y], x] + y*D[w[x, y], y] == b*w[x, y] + c*x^n*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1030*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*w[x, y] + b*x^n*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1031*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*Sqrt[x^2+y^2]*w[x,y] + b*x^n*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1032*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*x^n*y^m*w[x,y] + p*x^k*y^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1033*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*(x^n+p*y^m)*w[x,y] + q*x^k*y^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1034*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = x^2*D[w[x, y], x] + a*x*y*D[w[x, y], y] == b*y^2*w[x,y] + c*x^n*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1035*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = x^2*D[w[x, y], x] + x*y*D[w[x, y], y] == y^2*(a*x+b*y)*w[x,y] + c*x^n*y^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1036*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*x^n*D[w[x, y], x] + b*x^m*y*D[w[x, y], y] == c*x^p*y^q*w[x,y] + s*x^gamma*y^delta+d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1037*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*x^n*D[w[x, y], x] + (b*x^m*y+x*x^k)*D[w[x, y], y] == s*x^p*y^q*w[x,y] + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1038*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*x^n*D[w[x, y], x] + b*x^m*y^k*D[w[x, y], y] == c*w[x,y] + s*x^p*y^q+d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1039*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = a*y^k*D[w[x, y], x] + b*x^n*D[w[x, y], y] == c*w[x,y] + s*x^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1040*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*Exp[lambda*x]+s*Exp[mu*y])*w[x,y] + k*Exp[nu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1041*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Exp[alpha*x+beta*y]*w[x,y] + k*Exp[gamma*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1042*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*Exp[beta*x]*D[w[x, y], y] == c*Exp[gamma*y]*w[x,y] + s*Exp[mu*x+delta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1043*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[beta*x]*D[w[x, y], x] + (b*Exp[gamma*x]+c*Exp[lambda*y])*D[w[x, y], y] == s*w[x,y] + k*Exp[mu*x+delta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1044*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[beta*x]*D[w[x, y], x] + (b*Exp[gamma*x]+c*Exp[lambda*y])*D[w[x, y], y] == s*Exp[mu*x+delta*y]*w[x,y]+k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1045*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[beta*x]*D[w[x, y], x] + b*Exp[gamma*x+lambda*y]*D[w[x, y], y] == c*Exp[sigma*y]*w[x,y]+k*Exp[mu*x+delta*y]+d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1046*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*Exp[beta*x]*D[w[x, y], y] == c*w[x,y]+s*Exp[gamma*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1047*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*x^(beta*x)*D[w[x, y], y] == c*Exp[gamma*x]*w[x,y]+s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; (*----------------------------*) (*PDE number 1048*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y+b*x^n)*D[w[x, y], y] == c*w[x,y]+k*Exp[gamma*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1049*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y+b*Exp[beta*x])*D[w[x, y], y] == c*w[x,y]+k*Exp[gamma*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1050*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y], x] + (a*Exp[lambda*x]*y+b*Exp[beta*x])*D[w[x, y], y] == c*w[x,y]+k*x^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1051*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y], x] + (a*Exp[lambda*y]+b*x^k)*D[w[x, y], y] == c*w[x,y]+k*Exp[gamma*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1052*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Exp[lambda*x+mu*y]*w[x,y]+b*Exp[nu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1053*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == (a*y*Exp[lambda*x]+b*x*Exp[mu*y])*w[x,y]+c*Exp[nu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1054*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*y^k*D[w[x, y], x] + b*Exp[lambda*x]*D[w[x, y], y] == w[x,y]+c*Exp[beta*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1055*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[lambda*x]*D[w[x, y], x] + b*y*D[w[x, y], y] == w[x,y]+c*Exp[lambda*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1056*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[lambda*y]*D[w[x, y], x] + b*x^k*D[w[x, y], y] == w[x,y]+c*Exp[beta*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1057*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Exp[lambda*y]*D[w[x, y], x] + b*Exp[beta*x]*D[w[x, y], y] == w[x,y]+c*x^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1058*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+Sinh[lambda*x]^k*Sinh[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1059*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Sinh[lambda*x]^k*w[x,y]+ s*Sinh[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1060*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c1*Sinh[lambda1*x]^n1 + c2*Sinh[lambda2*y]^n2)*w[x,y] + s1*Sinh[beta1*x]^k1+ s2*Sinh[beta2*y]^k2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1061*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Sinh[lambda*x]^n*D[w[x, y], x] + b*Sinh[mu*x]^m*D[w[x, y], y] == c*Sinh[nu*x]*w[x,y]+p*Sinh[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1062*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Sinh[lambda*x]^n*D[w[x, y], x] + b*Sinh[mu*x]^m*D[w[x, y], y] == c*Sinh[nu*y]*w[x,y]+p*Sinh[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1063*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+Cosh[lambda*x]^k*Cosh[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1064*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Cosh[lambda*x]^k*w[x,y]+ s*Cosh[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1065*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c1*Cosh[lambda1*x]^n1 + c2*Cosh[lambda2*y]^n2)*w[x,y] + s1*Cosh[beta1*x]^k1+ s2*Cosh[beta2*y]^k2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1066*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Cosh[lambda*x+my*y]+b*Cosh[nu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1067*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Cosh[lambda*x]^n*D[w[x, y], x] + b*Cosh[mu*x]^m*D[w[x, y], y] == c*Cosh[nu*x]^k+p*Cosh[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1068*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Cosh[lambda*x]^n*D[w[x, y], x] + b*Cosh[mu*x]^m*D[w[x, y], y] == c*Cosh[nu*y]^k+p*Cosh[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1069*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+Tanh[lambda*x]^k*Tanh[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1070*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Tanh[lambda*x]^k*w[x,y]+ s*Tanh[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1071*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c1*Tanh[lambda1*x]^n1 + c2*Tanh[lambda2*y]^n2)*w[x,y] + s1*Tanh[beta1*x]^k1+ s2*Tanh[beta2*y]^k2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1072*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Tanh[lambda*x]^n*D[w[x, y], x] + b*Tanh[mu*x]^m*D[w[x, y], y] == c*Tanh[nu*x]*w[x,y]+p*Tanh[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1073*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Tanh[lambda*x]^n*D[w[x, y], x] + b*Tanh[mu*x]^m*D[w[x, y], y] == c*Tanh[nu*y]*w[x,y]+p*Tanh[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1074*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+Coth[lambda*x]^k*Coth[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1075*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Coth[lambda*x]^k*w[x,y]+ s*Coth[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1076*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c1*Coth[lambda1*x]^n1 + c2*Coth[lambda2*y]^n2)*w[x,y] + s1*Coth[beta1*x]^k1+ s2*Coth[beta2*y]^k2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1077*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Coth[lambda*x]^n*D[w[x, y], x] + b*Coth[mu*x]^m*D[w[x, y], y] == c*Coth[nu*x]*w[x,y]+p*Coth[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1078*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Coth[lambda*x]^n*D[w[x, y], x] + b*Coth[mu*x]^m*D[w[x, y], y] == c*Coth[nu*y]*w[x,y]+p*Coth[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1079*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*Sinh[lambda*x]^k+c2*Cosh[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1080*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ Sinh[lambda*x]^k*Cosh[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1081*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ k*Tanh[lambda*x]+s*coth[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1082*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*Sinh[lambda*x]*D[w[x, y], y] == c*w[x,y]+ k*Cosh[mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1083*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Sinh[lambda*x]^n*D[w[x, y], x] + b*Cosh[mu*x]^m*D[w[x, y], y] == c*Cosh[nu*x]^k*w[x,y]+ p*Sinh[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1084*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Tanh[lambda*x]^n*D[w[x, y], x] + b*Coth[mu*x]^m*D[w[x, y], y] == c*Tanh[nu*y]^k*w[x,y]+ p*Coth[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1085*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ Log[lambda*x]^k*Log[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1086*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*Log[lambda*x]^k*w[x,y]+s*Log[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1087*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == ( c1*Log[lambda1*x]^n1 +c2*Log[lambda2*y]^n2)*w[x,y] + s1*Log[beta1*x]^k1+s2*Log[beta2*y]*k2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1088*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Log[lambda*x]*D[w[x, y], x] + b*Log[mu*y]*D[w[x, y], y] == c*w[x,y]+k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1089*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Log[lambda*x]^n*D[w[x, y], x] + b*Log[mu*x]^m*D[w[x, y], y] == c*Log[nu*x]^k*w[x,y]+p*Log[beta*y]^s+q; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1090*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Log[lambda*x]^n*D[w[x, y], x] + b*Log[mu*x]^m*D[w[x, y], y] == c*Log[nu*y]^k*w[x,y]+p*Log[beta*x]^s+q; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1091*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+c1*x^k+c2*Log[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1092*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+x^k*Log[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1093*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x^k*D[w[x, y], x] + b*x^n*D[w[x, y], y] == c*w[x,y]+s*Log[beta*x]^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1094*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x^n*D[w[x, y], x] + b*y^k*D[w[x, y], y] == c*w[x,y]+s*Log[beta*x]^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1095*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x^n*D[w[x, y], x] + b*Log[lambda*x]^n*D[w[x, y], y] == c*w[x,y]+s*x^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1096*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*y^k*D[w[x, y], x] + b*x^n*D[w[x, y], y] == c*w[x,y]+s*Log[beta*x]^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1097*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*y^k*D[w[x, y], x] + b*Log[lambda*x]^n*D[w[x, y], y] == c*w[x,y]+s*x^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1098*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ k*Sin[lambda*x+mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1099*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*Sin[lambda*x]^k+c2*Sin[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1100*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ Sin[lambda*x]^k*Sin[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1101*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*w[x,y]+ k*Sin[lambda*x+beta*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1102*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Sin[lambda*x+beta*y]*w[x,y]+ b*Sin[nu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1103*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Sin[lambda*x]^n*D[w[x, y], x] + b*Sin[mu*x]^m*D[w[x, y], y] == c*Sin[nu*x]^k*w[x,y]+ p*Sin[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1104*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Sin[lambda*x]^n*D[w[x, y], x] + b*Sin[mu*x]^m*D[w[x, y], y] == c*Sin[nu*y]^k*w[x,y]+ p*Sin[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1105*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ k*Cos[lambda*x+mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1106*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*Cos[lambda*x]^k + c2*Cos[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1107*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ Cos[lambda*x]^k * Cos[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1108*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*w[x,y]+ k*Cos[lambda*x+mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1109*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == a*x*Cos[lambda*x+mu*y]*w[x,y]+b*Cos[nu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1110*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Cos[lambda*x]^n*D[w[x, y], x] + b*Cos[mu*x]^m*D[w[x, y], y] == c*Cos[nu*x]^k*w[x,y]+p*Cos[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1111*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+k*Tan[lambda*x+mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1112*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*Tan[lambda*x]^k + c2*Tan[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1113*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ Tan[lambda*x]^k * Tan[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1114*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*Tan[mu*y]*D[w[x, y], y] == c*Tan[lambda*x]*w[x,y]+k*Tan[nu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1115*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*w[x,y]+k*Tan[lambda*x+nu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1116*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Tan[lambda*x]^n*D[w[x, y], x] + b*Tan[mu*x]^m*D[w[x, y], y] == c*Tan[nu*x]^k*w[x,y]+p*Tan[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1117*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Tan[lambda*x]^n*D[w[x, y], x] + b*Tan[mu*x]^m*D[w[x, y], y] == c*Tan[nu*y]^k*w[x,y]+p*Tan[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1118*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+k*Cot[lambda*x+mu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1119*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*Cot[lambda*x]^k + c2*Cot[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1120*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ Cot[lambda*x]^k * Cot[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1121*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*Cot[mu*y]*D[w[x, y], y] == c*Cot[lambda*x]*w[x,y]+k*Cot[nu*x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1122*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*w[x,y]+k*Cot[lambda*x+nu*y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1123*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Cot[lambda*x]^n*D[w[x, y], x] + b*Cot[mu*x]^m*D[w[x, y], y] == c*Cot[nu*x]^k*w[x,y]+p*Cot[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1124*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Cot[lambda*x]^n*D[w[x, y], x] + b*Cot[mu*x]^m*D[w[x, y], y] == c*Cot[nu*y]^k*w[x,y]+p*Cot[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1125*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+c1*Sin[lambda*x]^k+c2*Cos[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1126*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+Sin[lambda*x]^k*Cos[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1127*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*Sin[mu*y]*D[w[x, y], y] == c*Sin[lambda*x]*w[x,y]+k*Cos[nu*x]+s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1128*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*Sin[mu*y]*D[w[x, y], y] == c*Sin[lambda*x]*w[x,y]+k*Tan[nu*x]+s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1129*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*Tan[mu*y]*D[w[x, y], y] == c*Tan[lambda*x]*w[x,y]+k*Cot[nu*x]+s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1130*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Sin[lambda*x]^n*D[w[x, y], x] + b*Cos[mu*x]^m*D[w[x, y], y] == c*Cos[nu*x]^k*w[x,y]+p*Sin[beta*y]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1131*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*Tan[lambda*x]^n*D[w[x, y], x] + b*Cot[mu*x]^m*D[w[x, y], y] == c*Tan[nu*x]^k*w[x,y]+p*Cot[beta*x]^s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1132*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*ArcSin[lambda*x]^k+c2*ArcSin[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1133*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ ArcSin[lambda*x]^k*ArcSin[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1134*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == ( c1*ArcSin[lambda1*x] + c2*ArcSin[lambda2*y])*w[x,y]+ s1*ArcSin[beta1*x]^n+ s2*ArcSin[beta2*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1135*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*ArcSin[mu*x]^m*D[w[x, y], y] == c*ArcSin[nu*x]^k*w[x,y]+p*ArcSin[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1136*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*ArcSin[mu*x]^m*D[w[x, y], y] == c*ArcSin[nu*y]^k*w[x,y]+p*ArcSin[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1137*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*ArcCos[lambda*x]^k+c2*ArcCos[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1138*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ ArcCos[lambda*x]^k*ArcCos[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1139*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == ( c1*ArcCos[lambda1*x] + c2*ArcCos[lambda2*y])*w[x,y]+ s1*ArcCos[beta1*x]^n+ s2*ArcCos[beta2*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1140*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*ArcCos[mu*x]^m*D[w[x, y], y] == c*ArcCos[nu*x]^k*w[x,y]+p*ArcCos[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1141*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*ArcCos[mu*x]^m*D[w[x, y], y] == c*ArcCos[nu*y]^k*w[x,y]+p*ArcCos[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1142*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*ArcTan[lambda*x]^k+c2*ArcTan[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1143*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ ArcTan[lambda*x]^k*ArcTan[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1144*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == ( c1*ArcTan[lambda1*x] + c2*ArcTan[lambda2*y])*w[x,y]+ s1*ArcTan[beta1*x]^n+ s2*ArcTan[beta2*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1145*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*ArcTan[mu*x]^m*D[w[x, y], y] == c*ArcTan[nu*x]^k*w[x,y]+p*ArcTan[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1146*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*ArcTan[mu*x]^m*D[w[x, y], y] == c*ArcTan[nu*y]^k*w[x,y]+p*ArcTan[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1147*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == w[x,y]+ c1*ArcCot[lambda*x]^k+c2*ArcCot[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1148*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+ ArcCot[lambda*x]^k*ArcCot[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1149*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == ( c1*ArcCot[lambda1*x] + c2*ArcCot[lambda2*y])*w[x,y]+ s1*ArcCot[beta1*x]^n+ s2*ArcCot[beta2*y]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1150*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*ArcCot[mu*x]^m*D[w[x, y], y] == c*ArcCot[nu*x]^k*w[x,y]+p*ArcCot[beta*y]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1151*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*ArcCot[mu*x]^m*D[w[x, y], y] == c*ArcCot[nu*y]^k*w[x,y]+p*ArcCot[beta*x]^n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1152*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == f[x]*w[x,y]+g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1153*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (c*y+k)*w[x,y]+f[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1154*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == f[x]*y*w[x,y]+g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1155*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == f[x]*w[x,y]+g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1156*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + (a+y+b)*D[w[x, y], y] == c*w[x,y]+g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1157*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + g[x]*D[w[x, y], y] == h[x]*w[x,y]+p[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1158*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + (g1[x]*y+g0[x])*D[w[x, y], y] == h1[x]*w[x,y]+h0[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1159*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + (g1[x]*y+g0[x])*D[w[x, y], y] == h2[x]*w[x,y]+h1[x]*y+h0[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1160*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + (g1[x]*y+g0[x]*y^k)*D[w[x, y], y] == h2[x]*w[x,y]+h1[x]*y^n+h0[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1161*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + (g1[x]+g0[x]*Exp[lambda*y])*D[w[x, y], y] == h2[x]*w[x,y]+h1[x]*Exp[beta*y]+h0[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1162*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f1[x]*y^k*D[w[x, y], x] + f2[x]*D[w[x, y], y] == g[x]*w[x,y]+h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1163*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f1[x]*Exp[lambda*y]*D[w[x, y], x] + f2[x]*D[w[x, y], y] == g[x]*w[x,y]+h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1164*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+f[x]*g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1165*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*w[x,y]+x*f[x]+y*g[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1166*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == f[x]*w[x,y]+g[x]*h[x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1167*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == (f[x]+g[y])*w[x,y]+p[x]+q[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1168*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*w[x,y]+f[x]*g[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1169*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f1[x]*D[w[x, y], x] + f2[y]*D[w[x, y], y] == a*w[x,y]+g1[x]+g2[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1170*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y], x] + y*D[w[x, y], y] == x*f[y/x]*w[x,y]+g[x,y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1171*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == f[x,y]*w[x,y]+g[x,y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1172*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + g[x]*D[w[x, y], y] == h[x,y]*w[x,y]+F[x,y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1173*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + (g1[x]*y+g0[x])D[w[x, y], y] == h[x,y]*w[x,y]+F[x,y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1174*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + (g1[x]*y+g0[x]*y^k)D[w[x, y], y] == h[x,y]*w[x,y]+F[x,y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1175*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = f[x]*D[w[x, y], x] + (g1[x]*y+g0[x]*Exp[lambda*y])D[w[x, y], y] == h[x,y]*w[x,y]+F[x,y]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1176*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y,z], x] + b*D[w[x, y,z], y] +c*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1177*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y,z], x] + a*x*D[w[x, y,z], y] +b*y*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1178*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y,z], x] + b*y*D[w[x, y,z], y] +c*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1179*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y,z], x] + a*z*D[w[x, y,z], y] +b*y*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1180*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y,z], x] + a*y*D[w[x, y,z], y] +b*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1181*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y,z], x] + a*z*D[w[x, y,z], y] +b*y*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1182*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y,z], x] + (a*x+b*y)*D[w[x, y,z], y] +(alpha*x+beta*y+gamma*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1183*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*b*x*D[w[x, y,z], x] + (a*y+b*z)*(b*D[w[x, y,z], y] -a*D[w[x,y,z],z])==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1184*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*b*x*D[w[x, y,z], x] + b*(a*y+b*z)*D[w[x, y,z], y] +a*(a*y-b*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1185*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b^2*c*y*D[w[x, y,z], x] + a^2*c*x*D[w[x, y,z], y] -a*b*(a*x+b*y)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1186*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = c*z*D[w[x, y,z], x] + (a*x+b*y)*D[w[x, y,z], y] +(a*x+b*y+c*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1187*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b^2*c*z*D[w[x, y,z], x] - a^2*c*x*D[w[x, y,z], y] +a*b^2*y*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1188*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = (x+a)*D[w[x, y,z], x] + (y+b)*D[w[x, y,z], y] +(z+c)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1189*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = 2*b*c*(a*x-b*y)*D[w[x, y,z], x] -a*c*(a*x-b*y-c*z)*D[w[x, y,z], y] - a*b*(a*x -b*y-3*c*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1190*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*c*(y-z)*D[w[x, y,z], x] +a*c*(z-x)*D[w[x, y,z], y] + a*b*(x -y)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1191*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*c*(b*y-2*c*z)*D[w[x, y,z], x] +a*c*(3*c*z-a*x)*D[w[x, y,z], y] + a*b*(2*a*x -3*b*y)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1192*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = 2*b*c*(b*y-c*z)*D[w[x, y,z], x] -a*c*(4*a*x-3*b*y-c*z)*D[w[x, y,z], y] + 3*a*b*(4*a*x-b*y-3*c*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1193*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = (a*x+y-z)*D[w[x, y,z], x] -(x+a*y-z)*D[w[x, y,z], y] + (a-1)*(y-x)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1194*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = 2*b*c*(3*a*x-2*b*y+c*z)*D[w[x, y,z], x] -2*a*c(2*a*x-5*b*y+3*c*z)*D[w[x, y,z], y] + a*b(2*a*x-6*b*y+11*c*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1195*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = (A*x+c*y+b*z)*D[w[x, y,z], x] +(c*x+B*y+a*z)*D[w[x, y,z], y] +(b*x+a*y+C1*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1196*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = (a1*x+b1*y+c1*z+d1)*D[w[x, y,z], x] +(a2*x+b2*y+c2*z+d2)*D[w[x, y,z], y] +(a3*x+b3*y+c3*z+d3)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1197*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y,z], x] +(a1*x*y+b1*x^2+c1*x)*D[w[x, y,z], y] +(a2*x*y+b2*x^2+c2*x)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1198*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y,z], x] +(a1*x*y+b1*x^2+c1*x)*D[w[x, y,z], y] +(a2*x*z+b2*x^2+c2*x)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1199*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y,z], x] +(a1*x*y+b1*x^2+c1*x)*D[w[x, y,z], y] +(a2*y*z+b2*y^2+c2*y)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1200*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = D[w[x, y,z], x] +(a1*x+b1*y^2)*D[w[x, y,z], y] +(a2*x*z+b2*z^2)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1201*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*D[w[x, y,z], x] +x*z*D[w[x, y,z], y] -x*y*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1202*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = c*x*D[w[x, y,z], x] +c*y*D[w[x, y,z], y] +(a*x^2+b*y^2)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1203*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = c*z*D[w[x, y,z], x] -a*(2*a*x-b)*y*D[w[x, y,z], y] +a*(2*a*x-b)*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1204*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*c*x^2*D[w[x, y,z], x] -a*c*x*y*D[w[x, y,z], y] -b^2*y^2*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1205*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x^2*D[w[x, y,z], x] +b*y^2*D[w[x, y,z], y] +c*z^2*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1206*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*b*x^2*D[w[x, y,z], x] +c*z^2*D[w[x, y,z], y] +2*a*b*x*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1207*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*c*x*y*D[w[x, y,z], x] +a^2*c*x^2*D[w[x, y,z], y] -b*y*(2*a*x+c*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1208*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*c*x*y*D[w[x, y,z], x] +c^2*y*z*D[w[x, y,z], y] +b^2*y^2*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1209*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*y*D[w[x, y,z], x] +y*(y-a)*D[w[x, y,z], y] +z*(y-a)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1210*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*y^2*D[w[x, y,z], x] -a*x*y*D[w[x, y,z], y] +c*x*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1211*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = c*x*z*D[w[x, y,z], x] +2*a*x*y*D[w[x, y,z], y] -(2*a*x+c*z)*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1212*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = c*x*z*D[w[x, y,z], x] +c*y*z*D[w[x, y,z], y] +a*b*x*y*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1213*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = c*x*z*D[w[x, y,z], x] -c*y*z*D[w[x, y,z], y] +(b*y^2-a*x)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1214*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = c*x*z*D[w[x, y,z], x] -c*y*z*D[w[x, y,z], y] +(a*x^2+b*y^2)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1215*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*z*D[w[x, y,z], x] +y*z*D[w[x, y,z], y] +(a*x^2+a*y^2+b*z^2)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1216*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = 2*c*x*z*D[w[x, y,z], x] +2*c*y*z*D[w[x, y,z], y] +(c*z^2-a*x^2-b*y^2)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1217*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*c*y*z*D[w[x, y,z], x] +a*c*x*z*D[w[x, y,z], y] +a*b*x*y*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1218*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*c*(x^2-a^2)*D[w[x, y,z], x] +c*(b*x*y+a*c*z)*D[w[x, y,z], y] +b*(c*x*z + a*b*y)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1219*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*x*(b*y+c)*D[w[x, y,z], x] + (b^2*y^2-a*c*x )*D[w[x, y,z], y] + b^2*y*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1220*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*(b*y -c*z)*D[w[x, y,z], x] + y*(c*z-a*x)*D[w[x, y,z], y] + z*(a*x - b*y)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1221*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*(y+beta)*(z+gamma)*D[w[x, y,z], x] -b*(x+alpha)*(z+gamma)*D[w[x, y,z], y] - c*(x+alpha)*(y+beta)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1222*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*c*(a*c*x*z + b^2*y^2)*D[w[x, y,z], x] +a*c*(b*c*y*z-2*a^2*x^2)*D[w[x, y,z], y] - a*b*(2*a*b*x*y+c^2*z^2)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1223*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*(y^2+z^2)*D[w[x, y,z], x] +x*(b*z-a*y)*D[w[x, y,z], y] -x*(b*y + a*z)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1224*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*(b*y + c*z)^2*D[w[x, y,z], x] - a*x*(b*y + 2*c*z)*D[w[x, y,z], y] +a*b*x*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1225*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; f[n_]:= a[n] + b[n]*x + c[n]*y+ d[n]*z; pde =(f[0]*x - f[1])*D[w[x, y,z], x] +(f[0]*y-f[2])*D[w[x, y,z], y] +(f[0]*z -f[3])*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1226*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde =2*b^2*x*z*D[w[x, y,z], x] + b*y*(b^2*z^2 +1)*D[w[x, y,z], y] + a*x*y*(b*z +1)^2*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1227*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde =b*c*x*y^2*D[w[x, y,z], x] + 2*b*c*y^3*D[w[x, y,z], y] + 2*(c*y*z-a*x^2)^2*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1228*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*c*x*y^2*D[w[x, y,z], x] + a*c^2*x*z^2*D[w[x, y,z], y] - a*b*x*y^2*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1229*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*(b*y^2-c*z^2)*D[w[x, y,z], x] + y*(c*z^2-a*x^2)*D[w[x, y,z], y] + z*(a*x^2-b*y^2)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1230*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*y*(3*a*x^2+ b*y^2+c*z^2)*D[w[x, y,z], x] - 2*a*x*(a*x^2+c*z^2)*D[w[x, y,z], y] + 2*a*b*x*y*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1231*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = b*(a*(a^2*x^2+b^2*y^2-1)*x+ b*y )*D[w[x, y,z], x] +a*(b*(a^2*x^2+b^2*y^2-1)*y - a*x)*D[w[x, y,z], y] + 2*a*b*z*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1232*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*(b^3*y^3 - 2*a^3*x^3)*D[w[x, y,z], x] +y*(2*b^3*y^3 -a^3*x^3)*D[w[x, y,z], y] +9*z*(a^3*x^3-b^3*y^3)*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1233*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = a*x^2*(a*b*x*y-c^2*z^2)*D[w[x, y,z], x] +a*x*y*(a*b*x*y-c^2*z^2)*D[w[x, y,z], y] +b*y*z*(b*c*y*z+2*a^2*x^2) *D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1234*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*(c*z^4 - b*y^4)*D[w[x, y,z], x] +y*(a*x^4-2*c*z^4)*D[w[x, y,z], y] +z*(2*b*y^4-a*x^4) *D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1235*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y,z], x] +y*D[w[x, y,z], y] +a*Sqrt[x^2+y^2]*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1236*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = x*D[w[x, y,z], x] +y*D[w[x, y,z], y] +(z-a*Sqrt[x^2+y^2+z^2])*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1237*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; pde = z*Sqrt[y^2+z^2]*D[w[x, y,z], x] +a*z*Sqrt[x^2+z^2]*D[w[x, y,z], y] -(x*Sqrt[y^2+z^2]+a*y*Sqrt[x^2+z^2])*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1238*) ClearAll[w, x, y, z, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t,F,C1]; ClearAll[g1, g0, h2, h1, h0, f1, f2,sigma,lambda1,lambda2,n1,n2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, nu]; f[t_]:= a[6]*t^6+a[5]*t^5+a[4]*t^4+a[3]*t^3+a[2]*t^2+a[1]*t+a[0]; pde = (y-z)*Sqrt[f[x]]*D[w[x, y,z], x] +(z-x)*Sqrt[f[y]]*D[w[x, y,z], y] +(x-y)*Sqrt[f[z]]*D[w[x,y,z],z]==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x, y,z}], 60*10]]; sol = Simplify[sol]; (*----------------------------*) (*PDE number 1239*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == a*D[w[x, t], {x, 2}] + b*w[x, t]^2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1240*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == D[w[x, t], {x, 2}] + a*w[x, t]*(1 - w[x, t]); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1241*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == a*D[w[x, t], {x, 2}] - b*w[x, t]^3; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1242*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == D[w[x, t], {x, 2}] + a*w[x, t] - b*w[x, t]^3; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1243*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == a*D[w[x, t], {x, 2}] - b*w[x, t]^3 - c*w[x, t]^2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1244*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == D[w[x, t], {x, 2}] - w[x, t]*(1 - w[x, t])*(a - w[x, t]); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1245*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b3, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == a*D[w[x, t], {x, 2}] + b0 + b1*w[x, t] + b2*w[x, t]^2 + b3*w[x, t]^3; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1246*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b3, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == a*D[w[x, t], {x, 2}] + b*w[x, t]^k; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1247*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b3, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == D[w[x, t], {x, 2}] + a*w[x, t] + b*w[x, t]^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1248*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b3, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == D[w[x, t], {x, 2}] + a*w[x, t] + b*w[x, t]^m + c*w[x, t]^(2*m - 1); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1249*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b3, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12]; pde = D[w[x, t], t] == D[w[x, t], {x, 2}] + a*w[x, t]^(m - 1) + b*m*w[x, t]^m - m*b^2*w[x, t]^(2*m - 1); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]]; (*----------------------------*) (*PDE number 1250*) ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; ClearAll[g1, g0, h2, h1, h0, f1, f2]; ClearAll[a1, a0, b3, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, s1, s2]; pde = D[w[x, t], t] == a*D[w[x, t], {x, 2}] + s1*(b*x + c*t)^k + s2*w[x, t]^m; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]];