Internal problem ID [3015]
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]
\[ \boxed {x y^{\prime }-y=x} \] With initial conditions \begin {align*} [y \left (-1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve([x*diff(y(x),x)=x+y(x),y(-1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -\left (i \pi -\ln \left (x \right )-1\right ) x \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 16
DSolve[{x*y'[x]==x+y[x],y[-1]==-1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (\log (x)-i \pi +1) \]