Internal problem ID [2558]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x -y x -y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 10
dsolve([x*diff(y(x),x)=x*y(x)+y(x),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{x -1} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 12
DSolve[{x*y'[x]==x*y[x]+y[x],y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x-1} x \\ \end{align*}