64.20.5 problem 5

Internal problem ID [13648]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:54:18 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y&=8 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 8.382 (sec). Leaf size: 18

dsolve([diff(y(t),t$2)+4*y(t)=8,y(0) = 0, D(y)(0) = 6],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]+4*y[t]==8,{y[0]==0,Derivative[1][y][0]==6}},{y[t]},t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 \sin (2 t)-2 \cos (2 t)+2 \]