Section 6.4

1.Consider the following initial value problem:

y+25y={9, 0t6

0, t>6 y(0)=5, y(0)=0

UsingYfor the Laplace transform ofy(t), i.e.,Y=L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)?

2.Take the Laplace transform of the following initial value problem and solve forY(s)=L{y(t)}

y''-y'-32y=S(t) y(0)=0, y'(0)=0

where S is a periodic function defined by

S(t)={1,0t<10,1t<2,andS(t+2)=S(t)for allt0.

Hint:: Use the formula for the Laplace transform of a periodic function.

Y(s)=?

3.Consider the following initial value problem:

y+25y={9t,0t7

63,t>7 y(0)=0,y(0)=0

UsingYfor the Laplace transform ofy(t), i.e.,Y=L{y(t)}

find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)=?

4.Consider the following initial value problem:

y+81y={3t,0t<3

0,t3 y(0)=0,y(0)=0

UsingY for the Laplace transform ofy(t), i.e.,Y=L{y(t)}

find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)?