ODE
\[ (y(x)+x) y'(x)=x-y(x) \] ODE Classification
[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0226282 (sec), leaf count = 51
\[\left \{\left \{y(x)\to -\sqrt {e^{2 c_1}+2 x^2}-x\right \},\left \{y(x)\to \sqrt {e^{2 c_1}+2 x^2}-x\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 33
\[ \left \{ -{\frac {1}{2}\ln \left ( {\frac {-{x}^{2}+2\,xy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}} \right ) }-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[(x + y[x])*y'[x] == x - y[x],y[x],x]
Mathematica raw output
{{y[x] -> -x - Sqrt[E^(2*C[1]) + 2*x^2]}, {y[x] -> -x + Sqrt[E^(2*C[1]) + 2*x^2]}}
Maple raw input
dsolve((x+y(x))*diff(y(x),x) = x-y(x), y(x),'implicit')
Maple raw output
-1/2*ln((-x^2+2*x*y(x)+y(x)^2)/x^2)-ln(x)-_C1 = 0