50.9.3 problem 1(c)

Internal problem ID [7939]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:33:21 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+8*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos \left (2 \sqrt {2} x\right )+c_2 \sin \left (2 \sqrt {2} x\right ) \]