35.9.8 problem 4, using elementary method

Internal problem ID [6243]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 4, using elementary method
Date solved : Monday, January 27, 2025 at 01:49:54 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=-4 y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)=-4*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]==-4*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos (2 x)+c_2 \sin (2 x) \]