4.11.47 $2xy(x)y^{\prime }(x)=4(2x+1)x^2+y(x{)}^2$

ODE
$$2xy(x)y^{\prime }(x)=4(2x+1)x^2+y(x{)}^2$$ ODE Classification

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica ✓
cpu = 0.00829588 (sec), leaf count = 52

$$\{\{y(x)\to -\sqrt{x}\sqrt{c_1+4x^2+4x}\},\{y(x)\to \sqrt{x}\sqrt{c_1+4x^2+4x}\}\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 22

$$\{-4x^3+{\left(y\left(x\right)\right)}^2-\mathit{\_}\mathit{C}\mathit{1}x-4x^2=0\}$$ Mathematica raw input

DSolve[2*x*y[x]*y'[x] == 4*x^2*(1 + 2*x) + y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -(Sqrt[x]*Sqrt[4*x + 4*x^2 + C[1]])}, {y[x] -> Sqrt[x]*Sqrt[4*x + 4*x^
2 + C[1]]}}

Maple raw input

dsolve(2*x*y(x)*diff(y(x),x) = 4*x^2*(1+2*x)+y(x)^2, y(x),'implicit')

Maple raw output

-4*x^3+y(x)^2-_C1*x-4*x^2 = 0