67.3.1 problem Problem 2

Internal problem ID [14019]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 2
Date solved : Tuesday, January 28, 2025 at 06:12:54 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+9 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 9.309 (sec). Leaf size: 10

dsolve([diff(y(t),t$2)+9*y(t)=0,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 2 \cos \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 11

DSolve[{D[y[t],{t,2}]+9*y[t]==0,{y[0]==2,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 \cos (3 t) \]