71.9.8 problem 8

Internal problem ID [14487]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 06:42:18 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 16

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

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