4.17.25 \(y'(x)^2-(2 x y(x)+1) y'(x)+2 x y(x)=0\)

ODE
\[ y'(x)^2-(2 x y(x)+1) y'(x)+2 x y(x)=0 \] ODE Classification

[_quadrature]

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

Mathematica
cpu = 0.00333074 (sec), leaf count = 21

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

Maple
cpu = 0.007 (sec), leaf count = 16

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

DSolve[2*x*y[x] - (1 + 2*x*y[x])*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(y(x),x)^2-(1+2*x*y(x))*diff(y(x),x)+2*x*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(x^2), y(x) = x+_C1