ODE
\[ (a+x) (b+x) y'(x)=x y(x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0162494 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_1 e^{\frac {a \log (a+x)-b \log (b+x)}{a-b}}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( a+x \right ) ^{{\frac {a}{a-b}}} \left ( b+x \right ) ^{-{\frac {b}{a-b}}} \right \} \] Mathematica raw input
DSolve[(a + x)*(b + x)*y'[x] == x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^((a*Log[a + x] - b*Log[b + x])/(a - b))*C[1]}}
Maple raw input
dsolve((a+x)*(b+x)*diff(y(x),x) = x*y(x), y(x),'implicit')
Maple raw output
y(x) = _C1*(a+x)^(a/(a-b))*(b+x)^(-b/(a-b))