4.13.14 \(\left (x^2+y(x)^2+2 y(x)\right ) y'(x)+2 x=0\)

ODE
\[ \left (x^2+y(x)^2+2 y(x)\right ) y'(x)+2 x=0 \] 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

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

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

\[ \left \{ \left ({x}^{2}+ \left (y \relax (x ) \right ) ^{2} \right ) {{\rm e}^{y \relax (x ) }}+{\it \_C1}=0 \right \} \] 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