49.1.11 problem 5(a)

Internal problem ID [7590]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number : 5(a)
Date solved : Monday, January 27, 2025 at 03:06:53 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: 0.024 (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*}