78.1.5 problem 1 (e)

Internal problem ID [18060]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (e)
Date solved : Tuesday, January 28, 2025 at 11:23:38 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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