ODE
\[ y''(x)=f\left (y'(x)\right ) \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.250165 (sec), leaf count = 35
\[\left \{\left \{y(x)\to \int _1^x\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{f(K[1])}dK[1]\& \right ][c_1+K[2]]dK[2]+c_2\right \}\right \}\]
Maple ✓
cpu = 0.334 (sec), leaf count = 22
\[\left [y \left (x \right ) = \int \RootOf \left (x -\left (\int _{}^{\textit {\_Z}}\frac {1}{f \left (\textit {\_f} \right )}d \textit {\_f} \right )+\textit {\_C1} \right )d x +\textit {\_C2}\right ]\] Mathematica raw input
DSolve[y''[x] == f[y'[x]],y[x],x]
Mathematica raw output
{{y[x] -> C[2] + Inactive[Integrate][InverseFunction[Inactive[Integrate][f[K[1]]^(-1), {K[1], 1, #1}] & ][C[1] + K[2]], {K[2], 1, x}]}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = f(diff(y(x),x)), y(x))
Maple raw output
[y(x) = Int(RootOf(x-Intat(1/f(_f),_f = _Z)+_C1),x)+_C2]