81.1.4 problem 2

Internal problem ID [18599]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:03:38 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

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

\[ y \left (x \right ) = c_{1} \sin \left (m x \right )+c_{2} \cos \left (m x \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

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

\[ y(x)\to c_1 \cos (m x)+c_2 \sin (m x) \]