ODE
\[ y(x) y''(x)=-y(x) f'(x)+f(x) y'(x)+y'(x)^2+y(x)^3 \] ODE Classification
odeadvisor timed out
Book solution method
TO DO
Mathematica ✓
cpu = 0.558373 (sec), leaf count = 192
\[\left \{\left \{y(x)\to -\frac {\exp \left (c_2-\int _1^x\frac {y(K[3])^3+\left (c_1+\int _1^{K[3]}-\frac {y(K[1])^3-f'(K[1]) y(K[1])+f(K[1]) y'(K[1])}{y(K[1])^2}dK[1]\right ){}^2 y(K[3])^2-f'(K[3]) y(K[3])+f(K[3]) y'(K[3])}{y(K[3])^2 \left (c_1+\int _1^{K[3]}-\frac {y(K[1])^3-f'(K[1]) y(K[1])+f(K[1]) y'(K[1])}{y(K[1])^2}dK[1]\right )}dK[3]\right )}{\int _1^x-\frac {y(K[1])^3-f'(K[1]) y(K[1])+f(K[1]) y'(K[1])}{y(K[1])^2}dK[1]+c_1}\right \}\right \}\]
Maple ✗
cpu = 1.879 (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(f(x),x)*y(x)+y(x)^3, y(x))
Mathematica raw input
DSolve[y[x]*y''[x] == y[x]^3 - y[x]*f'[x] + f[x]*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -(E^(C[2] - Inactive[Integrate][(y[K[3]]^3 + y[K[3]]^2*(C[1] + Inactive[Integrate][-((y[K[1]]^3 - y[K[1]]*Derivative[1][f][K[1]] + f[K[1]]*Derivative[1][y][K[1]])/y[K[1]]^2), {K[1], 1, K[3]}])^2 - y[K[3]]*Derivative[1][f][K[3]] + f[K[3]]*Derivative[1][y][K[3]])/(y[K[3]]^2*(C[1] + Inactive[Integrate][-((y[K[1]]^3 - y[K[1]]*Derivative[1][f][K[1]] + f[K[1]]*Derivative[1][y][K[1]])/y[K[1]]^2), {K[1], 1, K[3]}])), {K[3], 1, x}])/(C[1] + Inactive[Integrate][-((y[K[1]]^3 - y[K[1]]*Derivative[1][f][K[1]] + f[K[1]]*Derivative[1][y][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(f(x),x)*y(x)+y(x)^3, 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(f(x),x)*y(x)+y(x)^3, y(x))