8.2 problem 4

Internal problem ID [4952]

Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.4, page 230
Problem number: 4.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+16 y-4 \left (\delta \left (t -3 \pi \right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 0] \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 22

dsolve([diff(y(t),t$2)+16*y(t)=4*Dirac(t-3*Pi),y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
 

\[ y \relax (t ) = 2 \cos \left (4 t \right )+\theta \left (t -3 \pi \right ) \sin \left (4 t \right ) \]

Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

DSolve[{y''[t]+16*y[t]==4*DiracDelta[t-3*Pi],{y[0]==2,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \theta (t-3 \pi ) \sin (4 t)+2 \cos (4 t) \\ \end{align*}