74.18.34 problem 40

Internal problem ID [16591]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 09:11:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+16 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-8 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

dsolve([diff(y(t),t$2)+16*y(t)=0,y(0) = 0, D(y)(0) = -8],y(t), singsol=all)
 

\[ y = -2 \sin \left (4 t \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 11

DSolve[{D[y[t],{t,2}]+16*y[t]==0,{y[0]==0,Derivative[1][y][0] ==-8}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -2 \sin (4 t) \]