4.11.46 $2xy(x)y^{\prime }(x)=x^2+y(x{)}^2$

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

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

Book solution method
The Bernoulli ODE

Mathematica ✓
cpu = 0.00717018 (sec), leaf count = 38

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

Maple ✓
cpu = 0.005 (sec), leaf count = 14

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

DSolve[2*x*y[x]*y'[x] == x^2 + y[x]^2,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x)^2-(x+_C1)*x = 0