4.24.15 \(f\left (x y'(x)^2\right )=y(x)-2 x y'(x)\)

ODE
\[ f\left (x y'(x)^2\right )=y(x)-2 x y'(x) \] ODE Classification

[`y=_G(x,y')`]

Book solution method
Change of variable

Mathematica ✓
cpu = 0.176837 (sec), leaf count = 42

\[\left \{\left \{y(x)\to f(c_1)-2 \sqrt {c_1} \sqrt {x},y(x)\to f(c_1)+2 \sqrt {c_1} \sqrt {x}\right \}\right \}\]

Maple ✓
cpu = 0.369 (sec), leaf count = 24

\[\left [y \left (x \right ) = \textit {\_C1} +2 \sqrt {x}\, \RootOf \left (-f \left (\textit {\_Z}^{2}\right )+\textit {\_C1} +\textit {\_C2} -2 \textit {\_Z} \right )\right ]\] Mathematica raw input

DSolve[f[x*y'[x]^2] == y[x] - 2*x*y'[x],y[x],x]

Mathematica raw output

{{y[x] -> -2*Sqrt[x]*Sqrt[C[1]] + f[C[1]], y[x] -> 2*Sqrt[x]*Sqrt[C[1]] + f[C[1]
]}}

Maple raw input

dsolve(f(x*diff(y(x),x)^2) = y(x)-2*x*diff(y(x),x), y(x))

Maple raw output

[y(x) = _C1+2*x^(1/2)*RootOf(-f(_Z^2)+_C1+_C2-2*_Z)]