4.42.11 $y^{″}(x)f(y^{\prime }(x))+g(y(x))y^{\prime }(x)+h(x)=0$

ODE
$$y^{″}(x)f(y^{\prime }(x))+g(y(x))y^{\prime }(x)+h(x)=0$$ 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

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{f}\left(\mathit{\_}\mathit{b}\right),[\{{\int }^{\mathit{\_}\mathit{f}\left(\mathit{\_}\mathit{b}\right)}g\left(\mathit{\_}\mathit{a}\right)d\mathit{\_}\mathit{a}+{\int }^{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{b}}\mathit{\_}\mathit{f}\left(\mathit{\_}\mathit{b}\right)}f\left(\mathit{\_}\mathit{a}\right)d\mathit{\_}\mathit{a}+\int h\left(\mathit{\_}\mathit{b}\right)\mathrm{d}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}=0\},\{\mathit{\_}\mathit{b}=x,\mathit{\_}\mathit{f}\left(\mathit{\_}\mathit{b}\right)=y\left(x\right)\},\{x=\mathit{\_}\mathit{b},y\left(x\right)=\mathit{\_}\mathit{f}\left(\mathit{\_}\mathit{b}\right)\}])\}$$ 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)}]
)