Internal problem ID [11669]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 8, Separable equations. Exercises page 72
Problem number: 8.3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{\prime }-k y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve(x*diff(y(x),x)=k*y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{k} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 16
DSolve[x*y'[x]==k*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^k y(x)\to 0 \end{align*}