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

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

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