Internal problem ID [10992]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 5(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+29 y-5 \left (\delta \left (t -\pi \right )\right )+5 \left (\delta \left (-2 \pi +t \right )\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+29*y(t)=5*Dirac(t-Pi)-5*Dirac(t-2*Pi),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -{\mathrm e}^{-2 t +2 \pi } \sin \left (5 t \right ) \left ({\mathrm e}^{2 \pi } \operatorname {Heaviside}\left (t -2 \pi \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 39
DSolve[{y''[t]+4*y'[t]+29*y[t]==5*DiracDelta[t-Pi]-5*DiracDelta[t-2*Pi],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -e^{2 \pi -2 t} \left (e^{2 \pi } \theta (t-2 \pi )+\theta (t-\pi )\right ) \sin (5 t) \\ \end{align*}