Simple step function, Laplace transform

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Homework Statement


A system is characterized by the equation y' + 3y = r' .

When the input is r(t) = u(t) - u(t-1), find y(t) by taking the inverse Laplace transform of Y(s).

Homework Equations


The Laplace transform integral
The Laplace transform of a derivative sF(s) - f(0)

The transfer function of the system Q = s/s+3

The impulse response qimp(t) = δ(t) - 3e-3t

The Attempt at a Solution


I'm really not sure what to do here. It seems like it should be simple enough but I feel like I am not understanding the question correctly. Any hints?
 
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Nevermind, got it.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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