20.21.9 problem Problem 9

Internal problem ID [3936]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 9
Date solved : Monday, January 27, 2025 at 08:04:45 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 2.843 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+4*y(t)=0,y(0) = 5, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = 5 \cos \left (2 t \right )+\frac {\sin \left (2 t \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 17

DSolve[{D[y[t],{t,2}]+4*y[t]==0,{y[0]==5,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 5 \cos (2 t)+\sin (t) \cos (t) \]