ODE
\[ a x+x (y(x)+2) y'(x)=0 \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0068614 (sec), leaf count = 50
\[\left \{\left \{y(x)\to -\sqrt {2} \sqrt {-a x+c_1+2}-2\right \},\left \{y(x)\to \sqrt {2} \sqrt {-a x+c_1+2}-2\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 23
\[ \left \{ {\frac { \left ( y \left ( x \right ) \right ) ^{2}+4\,y \left ( x \right ) +2\,a \left ( x+{\it \_C1} \right ) }{2\,a}}=0 \right \} \] Mathematica raw input
DSolve[a*x + x*(2 + y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -2 - Sqrt[2]*Sqrt[2 - a*x + C[1]]}, {y[x] -> -2 + Sqrt[2]*Sqrt[2 - a*x + C[1]]}}
Maple raw input
dsolve(x*(2+y(x))*diff(y(x),x)+a*x = 0, y(x),'implicit')
Maple raw output
1/2*(y(x)^2+4*y(x)+2*a*(x+_C1))/a = 0