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

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

[_linear]

Book solution method
Homogeneous equation

Mathematica
cpu = 0.00769079 (sec), leaf count = 22

\[\left \{\left \{y(x)\to \frac {a x}{1-b}+c_1 x^b\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 19

\[ \left \{ y \relax (x ) =-{\frac {ax}{-1+b}}+{x}^{b}{\it \_C1} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (a*x)/(1 - b) + x^b*C[1]}}

Maple raw input

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

Maple raw output

y(x) = -a/(-1+b)*x+x^b*_C1