50.1.4 problem 1(d)

Internal problem ID [7776]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:21:45 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 18

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

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