46.7.4 problem 21

Internal problem ID [7365]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number : 21
Date solved : Monday, January 27, 2025 at 02:51:01 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.472 (sec). Leaf size: 26

dsolve([diff(y(t),t$2)+9*y(t)=piecewise(0<t and t<Pi,8*sin(t),t>Pi,0),y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
 

\[ y = 4 \left (\left \{\begin {array}{cc} \sin \left (t \right ) \cos \left (t \right )^{2} & t <\pi \\ \frac {\sin \left (3 t \right )}{3} & \pi \le t \end {array}\right .\right ) \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 30

DSolve[{D[y[t],{t,2}]+9*y[t]==Piecewise[{{8*Sin[t],0<t<Pi},{0,t>Pi}}],{y[0]==0,Derivative[1][y][0] ==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {4}{3} \sin (3 t) & t>\pi \lor t\leq 0 \\ \sin (t)+\sin (3 t) & \text {True} \\ \end {array} \\ \end {array} \]