Internal problem ID [2383]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.8.
page 710
Problem number: Problem 9.
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 }+3 y-\left (\delta \left (t -2\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+3*y(t)=Dirac(t-2),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-t}+\frac {\theta \left (t -2\right ) \left ({\mathrm e}^{2-t}-{\mathrm e}^{6-3 t}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 37
DSolve[{y''[t]+4*y'[t]+3*y[t]==DiracDelta[t-2],{y[0]==1,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{2-3 t} \left (e^{2 t}-e^4\right ) \theta (t-2)+e^{-t} \\ \end{align*}