4.825   y′(x)2 − (2xy (x) +1)y′(x )+ 2xy(x) = 0

ODE

y′(x)2 − (2xy(x)+ 1)y′(x)+ 2xy(x) = 0

ODE Classification

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for y′

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

{{            }               }
   y(x) → c1ex2 ,{y(x) → c1 +x }

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

{y (x) =-C1ex2,y(x) = x+-C1 }

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