ODE
\[ (y(x)+x) y'(x)+y(x)=0 \] ODE Classification
[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0217192 (sec), leaf count = 47
\[\left \{\left \{y(x)\to -\sqrt {e^{2 c_1}+x^2}-x\right \},\left \{y(x)\to \sqrt {e^{2 c_1}+x^2}-x\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 16
\[ \left \{ x+{\frac {y \left ( x \right ) }{2}}-{\frac {{\it \_C1}}{y \left ( x \right ) }}=0 \right \} \] Mathematica raw input
DSolve[y[x] + (x + y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -x - Sqrt[E^(2*C[1]) + x^2]}, {y[x] -> -x + Sqrt[E^(2*C[1]) + x^2]}}
Maple raw input
dsolve((x+y(x))*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
x+1/2*y(x)-1/y(x)*_C1 = 0