D.E.: Reduction of Order: Non-shortcut method question

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I don't know what to do with the x^3*e^x on the left side of the page. In the example the instructor gave for a different problem, you couldn't solve for x. In this problem you can so what does that mean I need to do with it?

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Is this answer correct?
 
Yes, it is :)
 
So do you always just ignore the factor that doesn't contain the u(x) function like I just did in this example?
 

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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