4.5.31 $(a+x)y^{\prime }(x)=bx$

ODE
$$(a+x)y^{\prime }(x)=bx$$ ODE Classification

[_quadrature]

Book solution method
Separable ODE, Dependent variable missing

Mathematica ✓
cpu = 0.00477031 (sec), leaf count = 19

$$\left\{\{y(x)\to -ab\log (a+x)+bx+c_1\}\right\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 17

$$\{y\left(x\right)=-\ln (a+x)ab+bx+\mathit{\_}\mathit{C}\mathit{1}\}$$ 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