Internal problem ID [4385]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page
564
Problem number: 1, using elementary method.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{\prime }-x y-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 9
dsolve(x*diff(y(x),x)=x*y(x)+y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} c_{1} x \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 17
DSolve[x*y'[x]==x*y[x]+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x x \\ y(x)\to 0 \\ \end{align*}