(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.
y^('')-7y^(')=delta (t-2),y(0)=1,y^(')(0)=0.
a. Find the Laplace transform of the solution.
Y(s)=L{y(t)}
b. Obtain the solution y(t).
y(t)=
c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t=2.
y(t)={( if 0<=t<2,),( if 2<=t<infty .):}
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.
y"-7y'=6(t-2),
y0=1,y0=0
a.Find the Laplace transform of the solution.
Y(s)=L{y(t)}=
b.Obtain the solution y(t)
y(t)=
c.Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2
if0t<2,
if2<t<