ODE
\[ f\left (y'(x),y''(x)\right )=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 1.11781 (sec), leaf count = 37
\[\left \{\left \{y(x)\to \int _1^x \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{\text {InverseFunction}[f,2,2][K[1],0]} \, dK[1]\& \right ]\left [K[2]+c_1\right ] \, dK[2]+c_2\right \}\right \}\]
Maple ✓
cpu = 0.091 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) =\int \!{\it RootOf} \left ( x-\int ^{{\it \_Z}}\! \left ( {\it RootOf} \left ( f \left ( {\it \_f},{\it \_Z} \right ) \right ) \right ) ^{-1}{d{\it \_f}}+{\it \_C1} \right ) \,{\rm d}x+{\it \_C2} \right \} \] 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