ODE
\[ (a+x) y'(x)=b x+y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.172931 (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 = 0.012 (sec), leaf count = 24
\[\left [y \left (x \right ) = \left (b \ln \left (a +x \right )+\frac {b a}{a +x}+\textit {\_C1} \right ) \left (a +x \right )\right ]\] 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))
Maple raw output
[y(x) = (b*ln(a+x)+b*a/(a+x)+_C1)*(a+x)]