74.10.10 problem 10

Internal problem ID [16215]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 08:57:26 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 30

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

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