Internal problem ID [2889]
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 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y=\delta \left (t -3\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 2.594 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)-4*y(t)=Dirac(t-3),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {Heaviside}\left (-3+t \right ) \sinh \left (2 t -6\right )}{2}+\frac {\sinh \left (2 t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 44
DSolve[{y''[t]-4*y[t]==DiracDelta[t-3],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{-2 (t+3)} \left (\left (e^{4 t}-e^{12}\right ) \theta (t-3)+e^6 \left (e^{4 t}-1\right )\right ) \]