4.12.28 $2x^{2}y(x)y^{\prime }(x)=x^2(2x+1)-y(x{)}^2$

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

[[_homogeneous, `class D`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica ✓
cpu = 0.0110721 (sec), leaf count = 43

$$\{\{y(x)\to -\sqrt{c_1{e}^{\frac{1}{x}}+x^2}\},\{y(x)\to \sqrt{c_1{e}^{\frac{1}{x}}+x^2}\}\}$$

Maple ✓
cpu = 0.008 (sec), leaf count = 20

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

-x^2-exp(1/x)*_C1+y(x)^2 = 0