Internal problem ID [2902]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 154.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -a x -b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(x*diff(y(x),x) = a*x+b*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {a x}{b -1}+x^{b} c_{1} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 22
DSolve[x y'[x]==a x + b y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a x}{1-b}+c_1 x^b \\ \end{align*}