ODE
\[ y(x) y''(x)=y(x) f''(x)-f(x) y'(x)-f(x) y(x)^3+y'(x)^2+y(x)^4 \] ODE Classification
odeadvisor timed out
Book solution method
TO DO
Mathematica ✓
cpu = 0.761412 (sec), leaf count = 220
\[\left \{\left \{y(x)\to -\frac {\exp \left (c_2-\int _1^x\frac {y(K[3])^4-f(K[3]) y(K[3])^3+\left (c_1+\int _1^{K[3]}\frac {f(K[1]) \left (y(K[1])^3+y'(K[1])\right )-y(K[1]) \left (y(K[1])^3+f''(K[1])\right )}{y(K[1])^2}dK[1]\right ){}^2 y(K[3])^2+f''(K[3]) y(K[3])-f(K[3]) y'(K[3])}{y(K[3])^2 \left (c_1+\int _1^{K[3]}\frac {f(K[1]) \left (y(K[1])^3+y'(K[1])\right )-y(K[1]) \left (y(K[1])^3+f''(K[1])\right )}{y(K[1])^2}dK[1]\right )}dK[3]\right )}{\int _1^x\frac {f(K[1]) \left (y(K[1])^3+y'(K[1])\right )-y(K[1]) \left (y(K[1])^3+f''(K[1])\right )}{y(K[1])^2}dK[1]+c_1}\right \}\right \}\]
Maple ✗
cpu = 2.191 (sec), leaf count = 0 , could not solve
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-f(x)*diff(y(x),x)+diff(diff(f(x),x),x)*y(x)-f(x)*y(x)^3+y(x)^4, y(x))
Mathematica raw input
DSolve[y[x]*y''[x] == -(f[x]*y[x]^3) + y[x]^4 - f[x]*y'[x] + y'[x]^2 + y[x]*f''[x],y[x],x]
Mathematica raw output
{{y[x] -> -(E^(C[2] - Inactive[Integrate][(-(f[K[3]]*y[K[3]]^3) + y[K[3]]^4 + y[K[3]]^2*(C[1] + Inactive[Integrate][(f[K[1]]*(y[K[1]]^3 + Derivative[1][y][K[1]]) - y[K[1]]*(y[K[1]]^3 + Derivative[2][f][K[1]]))/y[K[1]]^2, {K[1], 1, K[3]}])^2 - f[K[3]]*Derivative[1][y][K[3]] + y[K[3]]*Derivative[2][f][K[3]])/(y[K[3]]^2*(C[1] + Inactive[Integrate][(f[K[1]]*(y[K[1]]^3 + Derivative[1][y][K[1]]) - y[K[1]]*(y[K[1]]^3 + Derivative[2][f][K[1]]))/y[K[1]]^2, {K[1], 1, K[3]}])), {K[3], 1, x}])/(C[1] + Inactive[Integrate][(f[K[1]]*(y[K[1]]^3 + Derivative[1][y][K[1]]) - y[K[1]]*(y[K[1]]^3 + Derivative[2][f][K[1]]))/y[K[1]]^2, {K[1], 1, x}]))}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-f(x)*diff(y(x),x)+diff(diff(f(x),x),x)*y(x)-f(x)*y(x)^3+y(x)^4, y(x))
Maple raw output
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-f(x)*diff(y(x),x)+diff(diff(f(x),x),x)*y(x)-f(x)*y(x)^3+y(x)^4, y(x))