65.3.7 problem 8.3

Internal problem ID [13725]
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
Date solved : Tuesday, January 28, 2025 at 05:59:50 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=k y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 9

dsolve(x*diff(y(x),x)=k*y(x),y(x), singsol=all)
 

\[ y = c_{1} x^{k} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 16

DSolve[x*D[y[x],x]==k*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x^k \\ y(x)\to 0 \\ \end{align*}