ODE
\[ x^2+2 (y(x)+x) y'(x)+2 y(x)=0 \] ODE Classification
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
Book solution method
Exact equation
Mathematica ✓
cpu = 0.167358 (sec), leaf count = 53
\[\left \{\left \{y(x)\to -x-\sqrt {-\frac {x^3}{3}+x^2+c_1}\right \},\left \{y(x)\to -x+\sqrt {-\frac {x^3}{3}+x^2+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 51
\[\left [y \left (x \right ) = -x -\frac {\sqrt {-3 x^{3}+9 x^{2}-9 \textit {\_C1}}}{3}, y \left (x \right ) = -x +\frac {\sqrt {-3 x^{3}+9 x^{2}-9 \textit {\_C1}}}{3}\right ]\] Mathematica raw input
DSolve[x^2 + 2*y[x] + 2*(x + y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -x - Sqrt[x^2 - x^3/3 + C[1]]}, {y[x] -> -x + Sqrt[x^2 - x^3/3 + C[1]]}}
Maple raw input
dsolve(2*(x+y(x))*diff(y(x),x)+x^2+2*y(x) = 0, y(x))
Maple raw output
[y(x) = -x-1/3*(-3*x^3+9*x^2-9*_C1)^(1/2), y(x) = -x+1/3*(-3*x^3+9*x^2-9*_C1)^(1/2)]