4.17.17 \(y'(x)^2-2 (x-y(x)) y'(x)-4 x y(x)=0\)

ODE
\[ y'(x)^2-2 (x-y(x)) y'(x)-4 x y(x)=0 \] ODE Classification

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

Mathematica
cpu = 0.00340433 (sec), leaf count = 23

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

Maple
cpu = 0.006 (sec), leaf count = 18

\[ \left \{ y \relax (x ) ={\it \_C1}\,{{\rm e}^{-2\,x}},y \relax (x ) ={x}^{2}+{\it \_C1} \right \} \] Mathematica raw input

DSolve[-4*x*y[x] - 2*(x - y[x])*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]/E^(2*x)}, {y[x] -> x^2 + C[1]}}

Maple raw input

dsolve(diff(y(x),x)^2-2*(x-y(x))*diff(y(x),x)-4*x*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x^2+_C1, y(x) = _C1*exp(-2*x)