4.42.33 $f(y^{\prime }(x),y^{″}(x))=0$

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

[[_2nd_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 1.11781 (sec), leaf count = 37

$$\left\{\{y(x)\to {\int }_1^x\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{\text{InverseFunction}[f,2,2][K[1],0]}dK[1]\mathrm{\&}][K[2]+c_1]dK[2]+c_2\}\right\}$$

Maple ✓
cpu = 0.091 (sec), leaf count = 24

$$\{y\left(x\right)=\int \mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(x-{\int }^{\mathit{\_}\mathit{Z}}{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}\left(f(\mathit{\_}\mathit{f},\mathit{\_}\mathit{Z})\right)\right)}^{-1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2}\}$$ Mathematica raw input

DSolve[f[y'[x], y''[x]] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[2] + Integrate[InverseFunction[Integrate[InverseFunction[f, 2, 2][K[
1], 0]^(-1), {K[1], 1, #1}] & ][C[1] + K[2]], {K[2], 1, x}]}}

Maple raw input

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

Maple raw output

y(x) = Int(RootOf(x-Intat(1/RootOf(f(_f,_Z)),_f = _Z)+_C1),x)+_C2