ODE
\[ f\left (x,y''(x)\right )=0 \] ODE Classification
[[_2nd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 3.24072 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \int _1^x \left (\int _1^{K[2]} \text {InverseFunction}[f,2,2][K[1],0] \, dK[1]\right ) \, dK[2]+c_2 x+c_1\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) =\int \!\!\!\int \!{\it RootOf} \left ( f \left ( x,{\it \_Z} \right ) \right ) \,{\rm d}x\,{\rm d}x+{\it \_C1}\,x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[f[x, y''[x]] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1] + x*C[2] + Integrate[Integrate[InverseFunction[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),'implicit')
Maple raw output
y(x) = Int(Int(RootOf(f(x,_Z)),x),x)+_C1*x+_C2