ODE
\[ a y'(x)^2 f'(y(x))+f(y(x)) y''(x)+g(y(x))=0 \] ODE Classification
odeadvisor timed out
Book solution method
TO DO
Mathematica ✓
cpu = 0.527248 (sec), leaf count = 112
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {f(K[2])^a}{\sqrt {c_1+2 \int _1^{K[2]}-f(K[1])^{2 a-1} g(K[1])dK[1]}}dK[2]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {f(K[3])^a}{\sqrt {c_1+2 \int _1^{K[3]}-f(K[1])^{2 a-1} g(K[1])dK[1]}}dK[3]\& \right ][x+c_2]\right \}\right \}\]
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[g[y[x]] + a*f'[y[x]]*y'[x]^2 + f[y[x]]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][-(f[K[2]]^a/Sqrt[C[1] + 2*Inactive[Integrate][-(f[K[1]]^(-1 + 2*a)*g[K[1]]), {K[1], 1, K[2]}]]), {K[2], 1, #1}] & ][x + C[2]]}, {y[x] -> InverseFunction[Inactive[Integrate][f[K[3]]^a/Sqrt[C[1] + 2*Inactive[Integrate][-(f[K[1]]^(-1 + 2*a)*g[K[1]]), {K[1], 1, K[3]}]], {K[3], 1, #1}] & ][x + C[2]]}}
Maple raw input
dsolve(f(y(x))*diff(diff(y(x),x),x)+a*eval(diff(f(u),u),{u = y(x)})*diff(y(x),x)^2+g(y(x)) = 0, 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)})|