50.7.3 problem 1(c)

Internal problem ID [7907]
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 1.9. Reduction of Order. Page 38
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:31:48 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-k^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)-k^2*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-k x}+c_{2} {\mathrm e}^{k x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-k^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{k x}+c_2 e^{-k x} \]