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

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

[[_2nd_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.182262 (sec), leaf count = 39

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

Maple ✗
cpu = 0.353 (sec), leaf count = 0 , result contains DESol or ODESolStruc

\[[]\]

Mathematica raw input

DSolve[f[y'[x], y''[x]] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[2] + Inactive[Integrate][InverseFunction[Inactive[Integrate][Inverse
Function[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))

Maple raw output

[]