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 = 0.174685 (sec), leaf count = 23
\[\left \{\left \{y(x)\to c_1 e^{-2 x}\right \},\left \{y(x)\to x^2+c_1\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 18
\[[y \left (x \right ) = x^{2}+\textit {\_C1}, y \left (x \right ) = {\mathrm e}^{-2 x} \textit {\_C1}]\] 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))
Maple raw output
[y(x) = x^2+_C1, y(x) = exp(-2*x)*_C1]