82.1.4 problem Ex. 6

Internal problem ID [18726]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter I. Definitions. Formation of differential equation. Exercises at page 12
Problem number : Ex. 6
Date solved : Tuesday, January 28, 2025 at 12:12:26 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)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

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

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