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

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

[[_2nd_order, _quadrature]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.168227 (sec), leaf count = 34

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

Maple ✓
cpu = 0.106 (sec), leaf count = 17

\[[y \left (x \right ) = \int \int \RootOf \left (f \left (x , \textit {\_Z}\right )\right )d x d x +\textit {\_C1} x +\textit {\_C2}]\] Mathematica raw input

DSolve[f[x, y''[x]] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1] + x*C[2] + Inactive[Integrate][Inactive[Integrate][InverseFunctio
n[f, 2, 2][K[1], 0], {K[1], 1, K[2]}], {K[2], 1, x}]}}

Maple raw input

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

Maple raw output

[y(x) = Int(Int(RootOf(f(x,_Z)),x),x)+_C1*x+_C2]