Internal problem ID [12426]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y-y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 7
dsolve(y(x)-x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 14
DSolve[y[x]-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x \\ y(x)\to 0 \\ \end{align*}