Internal problem ID [4954]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+5 y-\left (\delta \left (-1+t \right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 28
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+5*y(t)=Dirac(t-1),y(0) = 0, D(y)(0) = 3],y(t), singsol=all)
\[ y \relax (t ) = 3 \,{\mathrm e}^{-2 t} \sin \relax (t )+{\mathrm e}^{-2 t +2} \theta \left (t -1\right ) \sin \left (t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 31
DSolve[{y''[t]+4*y'[t]+5*y[t]==DiracDelta[t-1],{y[0]==0,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-2 t} \left (3 \sin (t)-e^2 \theta (t-1) \sin (1-t)\right ) \\ \end{align*}