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

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

\[ \left \{ y \relax (x ) =-\ln \left (a+x \right ) ab+bx+{\it \_C1} \right \} \] 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