How to find the inverse Laplace transform of the following functions. 2 / (s^2 + 3s -4)answer is (2/5)e^t -  (2/5)e^-4t

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given that:

`y(s)= 2/(s^2 + 3s-4)`

Now we will factor the denominator.

`==gt y(s)= 2/((s+4)(s-1))`

Now we will write using partial froactions.

`==gt 2/((s+4)(s-1)) = A/(s+4) + B/(s-1) =`

`=gt A= -2/5 ==gt B= 2/5`

` ==gt y(s)= (-2/5) / (s+4) + (2/5)/(s-1) `

`==gt y(s)= (-2/5) 1/(s-(-4)) + (2/5) 1/(s-1)`

Now we know that:

if `y(s)= 1/(s-a) ==gt y(t)= e^(at)`

`==gt y(t)= (-2/5) e^(-4t) + (2/5)e^t`

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