Internal problem ID [2379]
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 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-\left (\delta \left (t -1\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 32
dsolve([diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=Dirac(t-1),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \left (-{\mathrm e}^{t -1}+{\mathrm e}^{2 t -2}\right ) \theta \left (t -1\right )+2 \,{\mathrm e}^{t}-{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 31
DSolve[{y''[t]-3*y'[t]+2*y[t]==DiracDelta[t-1],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t \left (\frac {\left (e^t-e\right ) \theta (t-1)}{e^2}-e^t+2\right ) \\ \end{align*}