4.13.14 $(x^2+y(x{)}^2+2y(x))y^{\prime }(x)+2x=0$

ODE
$$(x^2+y(x{)}^2+2y(x))y^{\prime }(x)+2x=0$$ ODE Classification

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.0522379 (sec), leaf count = 19

$$\text{Solve}[e^{y(x)}(x^2+y(x{)}^2)=c_1,y(x)]$$

Maple ✓
cpu = 0.016 (sec), leaf count = 17

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

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

Mathematica raw output

Solve[E^y[x]*(x^2 + y[x]^2) == C[1], y[x]]

Maple raw input

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

Maple raw output

(x^2+y(x)^2)*exp(y(x))+_C1 = 0