ODE
\[ (a+x) y'(x)=b x \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Dependent variable missing
Mathematica ✓
cpu = 0.00477031 (sec), leaf count = 19
\[\left \{\left \{y(x)\to -a b \log (a+x)+b x+c_1\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) =-\ln \left ( a+x \right ) ab+bx+{\it \_C1} \right \} \] Mathematica raw input
DSolve[(a + x)*y'[x] == b*x,y[x],x]
Mathematica raw output
{{y[x] -> b*x + C[1] - a*b*Log[a + x]}}
Maple raw input
dsolve((a+x)*diff(y(x),x) = b*x, y(x),'implicit')
Maple raw output
y(x) = -ln(a+x)*a*b+b*x+_C1