4.11.41 \((a+x) (b+x) y'(x)=x y(x)\)

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

\[ \left \{ y \relax (x ) ={\it \_C1}\, \left (a+x \right ) ^{{\frac {a}{a-b}}} \left (b+x \right ) ^{-{\frac {b}{a-b}}} \right \} \] 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))