73.20.5 problem 29.6 (e)

Internal problem ID [15614]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 29. Convolution. Additional Exercises. page 523
Problem number : 29.6 (e)
Date solved : Tuesday, January 28, 2025 at 08:03:10 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 9.454 (sec). Leaf size: 15

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

\[ y = -\frac {\sin \left (2 t \right )}{6}+\frac {\sin \left (t \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 15

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

\[ y(t)\to -\frac {1}{3} \sin (t) (\cos (t)-1) \]