ODE
\[ x^2+2 y(x) y'(x)+y(x)^2+2 x=0 \] ODE Classification
[[_homogeneous, `class D`], _rational, _Bernoulli]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.0101089 (sec), leaf count = 47
\[\left \{\left \{y(x)\to -\sqrt {c_1 e^{-x}-x^2}\right \},\left \{y(x)\to \sqrt {c_1 e^{-x}-x^2}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 18
\[ \left \{ {x}^{2}-{{\rm e}^{-x}}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{2}=0 \right \} \] Mathematica raw input
DSolve[2*x + x^2 + y[x]^2 + 2*y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-x^2 + C[1]/E^x]}, {y[x] -> Sqrt[-x^2 + C[1]/E^x]}}
Maple raw input
dsolve(2*y(x)*diff(y(x),x)+2*x+x^2+y(x)^2 = 0, y(x),'implicit')
Maple raw output
x^2-exp(-x)*_C1+y(x)^2 = 0