Internal problem ID [4953]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\left (\delta \left (-\pi +t \right )\right )+\delta \left (-2 \pi +t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 22
dsolve([diff(y(t),t$2)+y(t)=Dirac(t-Pi)-Dirac(t-2*Pi),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = -\sin \relax (t ) \left (\theta \left (-\pi +t \right )+\theta \left (-2 \pi +t \right )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 23
DSolve[{y''[t]+y[t]==DiracDelta[t-Pi]-DiracDelta[t-2*Pi],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -((\theta (t-2 \pi )+\theta (t-\pi )-1) \sin (t)) \\ \end{align*}