(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the Laplace transform method to solve the differential equation

y" -4y' +4y = e^2t subject to initial conditions y(0)=1, y'(0)=0

2. Relevant equations

3. The attempt at a solution

s^2Y(s) -sy(0) - y'(0) - 4[ sY(s) - y(0)] + 4Y(s)= L (e^2t)

Y(s) [s^2 -4s +4] - s -4 = 1/(s-2)

Y(s) [ (s-2)^2 ] = 1/(s-2) + s +4

Y(s) = 1/(s-2)^3 + s/(s-2)^2 + 4/(s-2)^2

Is this right, how do I find out the inverse laplace of Y(s) like for example 1/(s-2)^3 seems impossible!

Thanks.

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# Initial value problem (Laplace)

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