6.8.25 8.3
6.8.25.1 [1908] Problem 1
problem number 1908
Added Jan 1, 2020.
Problem Chapter 8.8.3.1, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ a w_x + b w_y + f(x,y) w_z = g(x,y) w \]
Mathematica ✓
ClearAll["Global`*"];
pde = a*D[w[x,y,z],x]+b*D[w[x,y,z],y]+f[x,y]*D[w[x,y,z],z]==g[x,y]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
\[\left \{\left \{w(x,y,z)\to \exp \left (\int _1^x\frac {g\left (K[2],y+\frac {b (K[2]-x)}{a}\right )}{a}dK[2]\right ) c_1\left (y-\frac {b x}{a},z-\int _1^x\frac {f\left (K[1],y+\frac {b (K[1]-x)}{a}\right )}{a}dK[1]\right )\right \}\right \}\]
Maple ✓
restart;
local gamma;
pde := a*diff(w(x,y,z),x)+ b*diff(w(x,y,z),y)+ f(x,y)*diff(w(x,y,z),z)=g(x,y)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
\[w \left (x , y , z\right ) = f_{1} \left (\frac {a y -b x}{a}, -\frac {\int _{}^{x}f \left (\textit {\_a} , \frac {a y -b \left (x -\textit {\_a} \right )}{a}\right )d \textit {\_a}}{a}+z \right ) {\mathrm e}^{\frac {\int _{}^{x}g \left (\textit {\_a} , \frac {a y -b \left (x -\textit {\_a} \right )}{a}\right )d \textit {\_a}}{a}}\]
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6.8.25.2 [1909] Problem 2
problem number 1909
Added Jan 1, 2020.
Problem Chapter 8.8.3.2, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ a w_x + b w_y + f(x,y) g(z) w_z = h(x,y) w \]
Mathematica ✗
ClearAll["Global`*"];
pde = a*D[w[x,y,z],x]+b*D[w[x,y,z],y]+f[x,y]*g[z]*D[w[x,y,z],z]==h[x,y]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✓
restart;
local gamma;
pde := a*diff(w(x,y,z),x)+ b*diff(w(x,y,z),y)+ f(x,y)*g(z)*diff(w(x,y,z),z)=h(x,y)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
\[w \left (x , y , z\right ) = f_{1} \left (\frac {a y -b x}{a}, -\int _{}^{x}f \left (\textit {\_a} , \frac {a y -b \left (x -\textit {\_a} \right )}{a}\right )d \textit {\_a} +a \int \frac {1}{g \left (z \right )}d z \right ) {\mathrm e}^{\frac {\int _{}^{x}h \left (\textit {\_a} , \frac {a y -b \left (x -\textit {\_a} \right )}{a}\right )d \textit {\_a}}{a}}\]
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6.8.25.3 [1910] Problem 3
problem number 1910
Added Jan 1, 2020.
Problem Chapter 8.8.3.3, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ x w_x + y w_y + (z+f(x,y)) w_z = g(x,y) w \]
Mathematica ✓
ClearAll["Global`*"];
pde = x*D[w[x,y,z],x]+y*D[w[x,y,z],y]+(z+f[x,y])*D[w[x,y,z],z]==g[x,y]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
\[\left \{\left \{w(x,y,z)\to \exp \left (\int _1^x\frac {g\left (K[2],\frac {y K[2]}{x}\right )}{K[2]}dK[2]\right ) c_1\left (\frac {y}{x},\frac {z}{x}-\int _1^x\frac {f\left (K[1],\frac {y K[1]}{x}\right )}{K[1]^2}dK[1]\right )\right \}\right \}\]
Maple ✓
restart;
local gamma;
pde := x*diff(w(x,y,z),x)+ y*diff(w(x,y,z),y)+ (z+f(x,y))*diff(w(x,y,z),z)=g(x,y)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
\[w \left (x , y , z\right ) = f_{1} \left (\frac {y}{x}, \frac {-\int _{}^{x}\frac {f \left (\textit {\_a} , \frac {y \textit {\_a}}{x}\right )}{\textit {\_a}^{2}}d \textit {\_a} x +z}{x}\right ) {\mathrm e}^{\int _{}^{x}\frac {g \left (\textit {\_a} , \frac {y \textit {\_a}}{x}\right )}{\textit {\_a}}d \textit {\_a}}\]
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6.8.25.4 [1911] Problem 4
problem number 1911
Added Jan 1, 2020.
Problem Chapter 8.8.3.4, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ a x w_x + b y w_y + f(x,y) g(z) w_z = h(x,y) w \]
Mathematica ✗
ClearAll["Global`*"];
pde = a*x*D[w[x,y,z],x]+b*y*D[w[x,y,z],y]+f[x,y]*g[z]*D[w[x,y,z],z]==h[x,y]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✓
restart;
local gamma;
pde := a*x*diff(w(x,y,z),x)+ b*y*diff(w(x,y,z),y)+ f(x,y)*g(z)*diff(w(x,y,z),z)=h(x,y)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
\[w \left (x , y , z\right ) = f_{1} \left (y \,x^{-\frac {b}{a}}, -\int _{}^{x}\frac {f \left (\textit {\_a} , y \,x^{-\frac {b}{a}} \textit {\_a}^{\frac {b}{a}}\right )}{\textit {\_a}}d \textit {\_a} +a \int \frac {1}{g \left (z \right )}d z \right ) {\mathrm e}^{\frac {\int _{}^{x}\frac {h \left (\textit {\_a} , y \,x^{-\frac {b}{a}} \textit {\_a}^{\frac {b}{a}}\right )}{\textit {\_a}}d \textit {\_a}}{a}}\]
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6.8.25.5 [1912] Problem 5
problem number 1912
Added Jan 1, 2020.
Problem Chapter 8.8.3.5, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ w_x + \left ( f_1(x) y+f_2(x) \right ) w_y + \left ( g_1(x,y) z+g_2(x,y) \right ) w_z = h(x,y,z) w \]
Mathematica ✓
ClearAll["Global`*"];
pde = D[w[x,y,z],x]+(f1[x]*y+f2[x])*D[w[x,y,z],y]+(g1[x,y]*z+g2[x,y])*D[w[x,y,z],z]==h[x,y,z]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
\[\left \{\left \{w(x,y,z)\to e^{\int _1^xh\left (K[5],e^{\int _1^{K[5]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[5]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right ),e^{\text {InverseFunction}[\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2],1,2]\left [\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\text {InverseFunction}[\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2],1,2]\left [\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\text {InverseFunction}[\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2],1,2]\left [\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\text {InverseFunction}[\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2],1,2]\left [\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^{K[5]}\text {g1}\left (K[3],e^{\int _1^{K[3]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[3]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[3]}\right ),\{K[3],1,K[5]\}\right ]dK[3]}\right ),\{K[3],1,K[4]\}\right ],\{K[3],1,K[5]\}\right ]}\right ),\{K[3],1,K[5]\}\right ]dK[3]}\right ),\{K[3],1,K[4]\}\right ],\{K[3],1,K[5]\}\right ]}\right ),\{K[3],1,K[5]\}\right ]dK[3]}\right ),\{K[3],1,K[4]\}\right ],\{K[3],1,K[5]\}\right ]}\right ),\{K[3],1,K[5]\}\right ]dK[3],\{K[3],1,K[4]\}\right ],\{K[3],1,K[5]\}\right ]-\int _1^x\text {g1}\left (K[3],e^{\int _1^{K[3]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[3]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[3]} \left (z-e^{\int _1^x\text {g1}\left (K[3],e^{\int _1^{K[3]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[3]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[3]} \int _1^xe^{-\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^x\text {g1}\left (K[3],e^{\int _1^{K[3]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[3]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[3]}\right ),\{K[3],1,x\}\right ]dK[3]} \text {g2}\left (K[4],e^{\int _1^{K[4]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[4]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[4]+e^{\int _1^x\text {g1}\left (K[3],e^{\int _1^{K[3]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[3]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[3]} \int _1^{K[5]}e^{-\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\text {InverseFunction}[\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2],1,2]\left [\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\text {InverseFunction}[\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2],1,2]\left [\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\text {InverseFunction}[\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2],1,2]\left [\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^{K[5]}\text {g1}\left (K[3],e^{\int _1^{K[3]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[3]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[3]}\right ),\{K[3],1,K[5]\}\right ]dK[3]}\right ),\{K[3],1,K[4]\}\right ],\{K[3],1,K[5]\}\right ]}\right ),\{K[3],1,K[5]\}\right ]dK[3]}\right ),\{K[3],1,K[4]\}\right ],\{K[3],1,K[5]\}\right ]}\right ),\{K[3],1,K[5]\}\right ]dK[3]}\right ),\{K[3],1,K[4]\}\right ],\{K[3],1,K[5]\}\right ]}\right ),\{K[3],1,K[5]\}\right ]dK[3]} \text {g2}\left (K[4],e^{\int _1^{K[4]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[4]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[4]\right )\right )dK[5]} c_1\left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2],e^{-\int _1^x\text {g1}\left (K[3],e^{\int _1^{K[3]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[3]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[3]} z-\int _1^xe^{-\int _1^{K[4]}\text {InverseFunction}[\text {Inactive}[\text {Integrate}],1,2]\left [\log \left (e^{\int _1^x\text {g1}\left (K[3],e^{\int _1^{K[3]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[3]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[3]}\right ),\{K[3],1,x\}\right ]dK[3]} \text {g2}\left (K[4],e^{\int _1^{K[4]}\text {f1}(K[1])dK[1]} \left (e^{-\int _1^x\text {f1}(K[1])dK[1]} y-\int _1^xe^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]+\int _1^{K[4]}e^{-\int _1^{K[2]}\text {f1}(K[1])dK[1]} \text {f2}(K[2])dK[2]\right )\right )dK[4]\right )\right \}\right \}\]
Maple ✓
restart;
local gamma;
pde := diff(w(x,y,z),x)+ (f__1(x)*y+f__2(x))*diff(w(x,y,z),y)+ (g__1(x,y)*z+g__2(x,y))*diff(w(x,y,z),z)=h(x,y,z)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
\[\text {Expression too large to display}\]
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6.8.25.6 [1913] Problem 6
problem number 1913
Added Jan 1, 2020.
Problem Chapter 8.8.3.6, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ w_x + \left ( f_1(x) y+f_2(x) y^k \right ) w_y + \left ( g_1(x,y) z+g_2(x,y) z^m \right ) w_z = h(x,y,z) w \]
Mathematica ✗
ClearAll["Global`*"];
pde = D[w[x,y,z],x]+(f1[x]*y+f2[x]*y^k)*D[w[x,y,z],y]+(g1[x,y]*z+g2[x,y]*z^m)*D[w[x,y,z],z]==h[x,y,z]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
$Aborted
Maple ✓
restart;
local gamma;
pde := diff(w(x,y,z),x)+ (f__1(x)*y+f__2(x)*y^k)*diff(w(x,y,z),y)+ (g__1(x,y)*z+g__2(x,y)*z^m)*diff(w(x,y,z),z)=h(x,y,z)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
\[\text {Expression too large to display}\]
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6.8.25.7 [1914] Problem 7
problem number 1914
Added Jan 1, 2020.
Problem Chapter 8.8.3.7, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ w_x + \left ( f_1(x) y+f_2(x) y^k \right ) w_y + \left ( g_1(x,y) z+g_2(x,y) e^{\lambda z} \right ) w_z = h(x,y,z) w \]
Mathematica ✗
ClearAll["Global`*"];
pde = D[w[x,y,z],x]+(f1[x]*y+f2[x]*y^k)*D[w[x,y,z],y]+(g1[x,y]*z+g2[x,y]*Exp[lambda*z])*D[w[x,y,z],z]==h[x,y,z]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✗
restart;
local gamma;
pde := diff(w(x,y,z),x)+ (f__1(x)*y+f__2(x)*y^k)*diff(w(x,y,z),y)+ (g__1(x,y)*z+g__2(x,y)*exp(lambda*z))*diff(w(x,y,z),z)=h(x,y,z)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
sol=()
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6.8.25.8 [1915] Problem 8
problem number 1915
Added Jan 1, 2020.
Problem Chapter 8.8.3.8, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ w_x + \left ( f_1(x) y+f_2(x) e^{\lambda y} \right ) w_y + \left ( g_1(x,y) z+g_2(x,y) z^k \right ) w_z = h(x,y,z) w \]
Mathematica ✗
ClearAll["Global`*"];
pde = D[w[x,y,z],x]+(f1[x]*y+f2[x]*Exp[lambda*y])*D[w[x,y,z],y]+(g1[x,y]*z+g2[x,y]*z^k)*D[w[x,y,z],z]==h[x,y,z]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✗
restart;
local gamma;
pde := diff(w(x,y,z),x)+ (f__1(x)*y+f__2(x)*exp(lambda*y))*diff(w(x,y,z),y)+ (g__1(x,y)*z+g__2(x,y)*z^k)*diff(w(x,y,z),z)=h(x,y,z)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
sol=()
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6.8.25.9 [1916] Problem 9
problem number 1916
Added Jan 1, 2020.
Problem Chapter 8.8.3.9, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ w_x + \left ( f_1(x) y+f_2(x) e^{\lambda y} \right ) w_y + \left ( g_1(x,y) z+g_2(x,y) e^{\beta z} \right ) w_z = h(x,y,z) w \]
Mathematica ✗
ClearAll["Global`*"];
pde = D[w[x,y,z],x]+(f1[x]*y+f2[x]*Exp[lambda*y])*D[w[x,y,z],y]+(g1[x,y]*z+g2[x,y]*Exp[beta*z])*D[w[x,y,z],z]==h[x,y,z]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✗
restart;
local gamma;
pde := diff(w(x,y,z),x)+ (f__1(x)*y+f__2(x)*exp(lambda*y))*diff(w(x,y,z),y)+ (g__1(x,y)*z+g__2(x,y)*exp(beta*z))*diff(w(x,y,z),z)=h(x,y,z)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
sol=()
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6.8.25.10 [1917] Problem 10
problem number 1917
Added Jan 1, 2020.
Problem Chapter 8.8.3.10, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ f_1(x) g_1(y) w_x + f_2(x) g_2(y) w_y + \left ( h_1(x,y) +h_2(x,y) z^m \right ) w_z = h_3(x,y,z) w \]
Mathematica ✗
ClearAll["Global`*"];
pde = f1[x]*g1[y]*D[w[x,y,z],x]+f2[x]*g2[y]*D[w[x,y,z],y]+(h1[x,y]+h2[x,y]*z^m)*D[w[x,y,z],z]==h3[x,y,z]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✓
restart;
local gamma;
pde := f__1(x)*g__1(y)*diff(w(x,y,z),x)+ f__2(x)*g__2(y)*diff(w(x,y,z),y)+ (h__1(x,y)*z+h__2(x,y)*z^m)*diff(w(x,y,z),z)=h__3(x,y,z)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
\[\text {Expression too large to display}\]
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6.8.25.11 [1918] Problem 11
problem number 1918
Added Jan 1, 2020.
Problem Chapter 8.8.3.11, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for \(w(x,y,z)\)
\[ f_1(x) g_1(y) w_x + f_2(x) g_2(y) w_y + \left ( h_1(x,y) +h_2(x,y) e^{\lambda z} \right ) w_z = h_3(x,y,z) w \]
Mathematica ✗
ClearAll["Global`*"];
pde = f1[x]*g1[y]*D[w[x,y,z],x]+f2[x]*g2[y]*D[w[x,y,z],y]+(h1[x,y]+h2[x,y]*Exp[lambda*z])*D[w[x,y,z],z]==h3[x,y,z]*w[x,y,z];
sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✗
restart;
local gamma;
pde := f__1(x)*g__1(y)*diff(w(x,y,z),x)+ f__2(x)*g__2(y)*diff(w(x,y,z),y)+ (h__1(x,y)*z+h__2(x,y)*exp(lambda*z))*diff(w(x,y,z),z)=h__3(x,y,z)*w(x,y,z);
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
sol=()