Question

what is the laplace transform of
5/2.e^t-3/2.e^-t

Answer 1

L{e^t} = 1/(s-1)
L{e^-t} = 1/(s+a)
L is a linear transform, so

L{5/2.e^t-3/2.e^-t} = 5/2 L{e^t} - 3/2 L{e^-t}
= 5/2 * 1/(s-1) - 3/2 * 1/(s+1)
= (s+4)/(s^2-1)

Answer 2

compute the inverse laplace transform 2S^2+13S+5/(s+3)(s-1)^2
i got 3e^t+5e^t+3e^t, not sure it correct