ODE
\[ (a+x) y'(x)=b x+y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.00989323 (sec), leaf count = 26
\[\left \{\left \{y(x)\to (a+x) \left (\frac {a b}{a+x}+b \log (a+x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) =b \left ( a+x \right ) \ln \left ( a+x \right ) + \left ( b+{\it \_C1} \right ) a+{\it \_C1}\,x \right \} \] Mathematica raw input
DSolve[(a + x)*y'[x] == b*x + y[x],y[x],x]
Mathematica raw output
{{y[x] -> (a + x)*((a*b)/(a + x) + C[1] + b*Log[a + x])}}
Maple raw input
dsolve((a+x)*diff(y(x),x) = b*x+y(x), y(x),'implicit')
Maple raw output
y(x) = b*(a+x)*ln(a+x)+(b+_C1)*a+_C1*x