4.42.32 \(f\left (y(x),y''(x)\right )=0\)

ODE
\[ f\left (y(x),y''(x)\right )=0 \] ODE Classification

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.409061 (sec), leaf count = 44

\[\text {Solve}\left [(x+c_2){}^2=\int _1^{y(x)}\frac {1}{\sqrt {c_1+2 \int _1^{K[2]}\text {InverseFunction}[f,2,2][K[1],0]dK[1]}}dK[2]{}^2,y(x)\right ]\]

Maple ✓
cpu = 0.55 (sec), leaf count = 33

\[\left [\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (\textit {\_Z}^{2}-\textit {\_C1} -2 \left (\int \RootOf \left (f \left (\textit {\_b} , \textit {\_Z}\right )\right )d \textit {\_b} \right )\right )}d \textit {\_b} -x -\textit {\_C2} = 0\right ]\] Mathematica raw input

DSolve[f[y[x], y''[x]] == 0,y[x],x]

Mathematica raw output

Solve[(x + C[2])^2 == Inactive[Integrate][1/Sqrt[C[1] + 2*Inactive[Integrate][In
verseFunction[f, 2, 2][K[1], 0], {K[1], 1, K[2]}]], {K[2], 1, y[x]}]^2, y[x]]

Maple raw input

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

Maple raw output

[Intat(1/RootOf(_Z^2-_C1-2*Int(RootOf(f(_b,_Z)),_b)),_b = y(x))-x-_C2 = 0]