##### 4.24.16 $$f\left (y(x),y'(x)\right )=0$$

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

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing

Mathematica
cpu = 0.173387 (sec), leaf count = 28

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

Maple
cpu = 0.071 (sec), leaf count = 28

$\left [y \left (x \right ) = \RootOf \left (f \left (\textit {\_Z} , 0\right )\right ), x -\left (\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (f \left (\textit {\_a} , \textit {\_Z}\right )\right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]$ Mathematica raw input

DSolve[f[y[x], y'[x]] == 0,y[x],x]

Mathematica raw output

{{y[x] -> InverseFunction[Inactive[Integrate][InverseFunction[f, 2, 2][K[1], 0]^
(-1), {K[1], 1, #1}] & ][x + C[1]]}}

Maple raw input

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

Maple raw output

[y(x) = RootOf(f(_Z,0)), x-Intat(1/RootOf(f(_a,_Z)),_a = y(x))-_C1 = 0]