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 = 0.172517 (sec), leaf count = 47
\[\left \{\left \{y(x)\to -x-\sqrt {x^2+e^{2 c_1}}\right \},\left \{y(x)\to -x+\sqrt {x^2+e^{2 c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 35
\[\left [y \left (x \right ) = -x -\sqrt {x^{2}+2 \textit {\_C1}}, y \left (x \right ) = -x +\sqrt {x^{2}+2 \textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = -x-(x^2+2*_C1)^(1/2), y(x) = -x+(x^2+2*_C1)^(1/2)]