ODE
\[ f(y(x)) y'(x)+g(y(x)) y'(x)^2+h(y(x))+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 50.4879 (sec), leaf count = 0 , could not solve
DSolve[h[y[x]] + f[y[x]]*Derivative[1][y][x] + g[y[x]]*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.559 (sec), leaf count = 59
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +g \left ( {\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+f \left ( {\it \_a} \right ) {\it \_b} \left ( {\it \_a} \right ) +h \left ( {\it \_a} \right ) =0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[h[y[x]] + f[y[x]]*y'[x] + g[y[x]]*y'[x]^2 + y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[h[y[x]] + f[y[x]]*Derivative[1][y][x] + g[y[x]]*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x)+g(y(x))*diff(y(x),x)^2+f(y(x))*diff(y(x),x)+h(y(x)) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a,[{diff(_b(_a),_a)*_b(_a)+g(_a)*_b(_a)^2+f(_a)*_b(_a)+h(_a) = 0}, {_a = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a),_a)+_C1, y(x) = _a}])