Internal problem ID [10991]
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(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y-3 \left (\delta \left (-1+t \right )\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+2*y(t)=3*Dirac(t-1),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 3 \,{\mathrm e}^{-t +1} \operatorname {Heaviside}\left (t -1\right ) \sin \left (t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 24
DSolve[{y''[t]+2*y'[t]+2*y[t]==3*DiracDelta[t-1],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -3 e^{1-t} \theta (t-1) \sin (1-t) \\ \end{align*}