Internal problem ID [10603]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x +y-y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve((x+y(x))- x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 12
DSolve[(x+y[x])- x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (\log (x)+c_1) \\ \end{align*}