ODE
\[ a y'(x)^2 f'(y(x))+f(y(x)) y''(x)+g(y(x))=0 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✓
cpu = 10.9666 (sec), leaf count = 108
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} -\frac {f(K[2])^a}{\sqrt {2 \int _1^{K[2]} g(K[1]) \left (-f(K[1])^{2 a-1}\right ) \, dK[1]+c_1}} \, dK[2]\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {f(K[3])^a}{\sqrt {2 \int _1^{K[3]} g(K[1]) \left (-f(K[1])^{2 a-1}\right ) \, dK[1]+c_1}} \, dK[3]\& \right ]\left [c_2+x\right ]\right \}\right \}\]
Maple ✗
cpu = 0.059 (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[Integrate[-(f[K[2]]^a/Sqrt[C[1] + 2*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[Integrate[f[K[3]]^a/Sqrt[C[1] + 2*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),'implicit')
Maple raw output
unable to handle composite functions containing y(x) or diff(y(x),x) as in eval(diff(f(u),u),{u = y(x)})