Internal problem ID [2506]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {-y+y^{\prime } x -x=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 14
dsolve([x*diff(y(x),x)=x+y(x),y(-1) = -1],y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \relax (x )+1-i \pi \right ) x \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 16
DSolve[{x*y'[x]==x+y[x],y[-1]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (\log (x)-i \pi +1) \\ \end{align*}