# ODE

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

• ODE -

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)

• ODE -

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

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