How to Solve a Nonhomogeneous 2nd Order DE with a Constant Term?

Sean77771
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Homework Statement



y'' + 9y = 2x2e3x + 5

Homework Equations



N/A

The Attempt at a Solution



I think the complementary solution yc = c1cos(3x) + c2sin(3x).

If not for that little +5 at the end of the right hand side, I'm pretty sure I could solve it. But I don't know how to include it in my solution.
 
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Try adding a constant to your specific solution.
 

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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