(3s+2)/((s^2)-1)

1.

Match each function with its Laplace Transform.

A. sin(t)

B. cos(t)

C. t^2

D. (e^2t)(sin(3t)

E. e^t

2.

B

C

A

E

D

Compute the Inverse Laplace Transform of the given function.

 

3.

The given function does not possess a Laplace Transform. 

(Hint: see definition of Laplace Transform)

 

A) True

B) False

4.

Use the  Laplace Transform to solve the given IVP.

(y’’)-(5*(y’))+(6*y)=u(t-1) y(0)=0 y’(0)=1

here      is a "unit step function".

 

5.

Use the Laplace Transform to solve the given IVP.

L^-1=(2.5*(e^t))+(0.5*(e^-t))

y(x)=(1/6)*(e^x-1)*((-e^x)*u(t-1)+(2*e^(2 x))*u(t-1)-u(t-1)+6*(e^(2 x)))

(y’’)-(2*(y’))=(e^t)*(sinh(t)) y(0)=0 y’(0)=0

 

y(t)=1/4 (e^(2 t) t+t-e^(2 t)+1)