ODE
\[ y''(x) f\left (y'(x)\right )+g(y(x)) y'(x)+h(x)=0 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.047685 (sec), leaf count = 0 , could not solve
DSolve[h[x] + g[y[x]]*Derivative[1][y][x] + f[Derivative[1][y][x]]*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 6.507 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_f} \left ( {\it \_b} \right ) ,[ \left \{ \int ^{{\it \_f} \left ( {\it \_b} \right ) }\!g \left ( {\it \_a} \right ) {d{\it \_a}}+\int ^{{\frac {\rm d}{{\rm d}{\it \_b}}}{\it \_f} \left ( {\it \_b} \right ) }\!f \left ( {\it \_a} \right ) {d{\it \_a}}+\int \!h \left ( {\it \_b} \right ) \,{\rm d}{\it \_b}+{\it \_C1}=0 \right \} , \left \{ {\it \_b}=x,{\it \_f} \left ( {\it \_b} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_b},y \left ( x \right ) ={\it \_f} \left ( {\it \_b} \right ) \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[h[x] + g[y[x]]*y'[x] + f[y'[x]]*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[h[x] + g[y[x]]*Derivative[1][y][x] + f[Derivative[1][y][x]]*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(f(diff(y(x),x))*diff(diff(y(x),x),x)+g(y(x))*diff(y(x),x)+h(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_f(_b),[{Intat(g(_a),_a = _f(_b))+Intat(f(_a),_a = diff(_f(_b),_b))+Int(h(_b),_b)+_C1 = 0}, {_b = x, _f(_b) = y(x)}, {x = _b, y(x) = _f(_b)}])