4.4.12 \(y(x) (a+b x)+x y'(x)=0\)

ODE
\[ y(x) (a+b x)+x y'(x)=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00612063 (sec), leaf count = 19

\[\left \{\left \{y(x)\to c_1 x^{-a} e^{-b x}\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 16

\[ \left \{ y \relax (x ) ={\it \_C1}\,{{\rm e}^{-bx}}{x}^{-a} \right \} \] Mathematica raw input

DSolve[(a + b*x)*y[x] + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]/(E^(b*x)*x^a)}}

Maple raw input

dsolve(x*diff(y(x),x)+(b*x+a)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(-b*x)*x^(-a)