4.42.35 $f(y(x),y^{\prime }(x),y^{″}(x))=0$

ODE
$$f(y(x),y^{\prime }(x),y^{″}(x))=0$$ ODE Classification

[[_2nd_order, _missing_x]]

Book solution method
TO DO

Mathematica ✗
cpu = 6.29472 (sec), leaf count = 0 , could not solve

DSolve[f[y[x], Derivative[1][y][x], Derivative[2][y][x]] == 0, y[x], x]

Maple ✓
cpu = 0.152 (sec), leaf count = 53

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

DSolve[f[y[x], y'[x], y''[x]] == 0,y[x],x]

Mathematica raw output

DSolve[f[y[x], Derivative[1][y][x], Derivative[2][y][x]] == 0, y[x], x]

Maple raw input

dsolve(f(y(x),diff(y(x),x),diff(diff(y(x),x),x)) = 0, y(x),'implicit')

Maple raw output

y(x) = ODESolStruc(_a,[{diff(_b(_a),_a)*_b(_a)-RootOf(f(_a,_b(_a),_Z)) = 0}, {_a
 = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a),_a)+_C1, y(x) = _a}])