ODE
\[ f(y(x)) y''(x)=y'(x)^2 f'(y(x))-g(x) f(y(x)) y'(x)-h(x) f(y(x))^2 \] ODE Classification
odeadvisor timed out
Book solution method
TO DO
Mathematica ✓
cpu = 0.276806 (sec), leaf count = 75
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{f(K[4])}dK[4]\& \right ]\left [\int _1^x-\exp \left (-\int _1^{K[5]}g(K[1])dK[1]\right ) \left (c_1+\int _1^{K[5]}\exp \left (\int _1^{K[3]}g(K[1])dK[1]\right ) h(K[3])dK[3]\right )dK[5]+c_2\right ]\right \}\right \}\]
Maple ✗
cpu = 0. (sec), leaf count = 0 , exception
unable to handle composite functions containing y(x) or diff(y(x),x) as in eval(diff(f(u),u),u = y(x))
Mathematica raw input
DSolve[f[y[x]]*y''[x] == -(f[y[x]]^2*h[x]) - f[y[x]]*g[x]*y'[x] + f'[y[x]]*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][f[K[4]]^(-1), {K[4], 1, #1}] & ][C[2] + Inactive[Integrate][-((C[1] + Inactive[Integrate][E^Inactive[Integrate][g[K[1]], {K[1], 1, K[3]}]*h[K[3]], {K[3], 1, K[5]}])/E^Inactive[Integrate][g[K[1]], {K[1], 1, K[5]}]), {K[5], 1, x}]]}}
Maple raw input
dsolve(f(y(x))*diff(diff(y(x),x),x) = eval(diff(f(u),u),{u = y(x)})*diff(y(x),x)^2-g(x)*f(y(x))*diff(y(x),x)-h(x)*f(y(x))^2, y(x))
Maple raw output
\verbunable to handle composite functions containing y(x) or diff(y(x),x) as in| eval(diff(f(u),u),{u = y(x)})|