How to Solve Linear Differential Equations with Trigonometric Functions?

blondie1234
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1. Find all real solutions: (dx/dt)-2x=cos(3t)



Homework Equations





3. I really don't know where to start here. Any advice to get me on my feet would be appreciated.
 
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blondie1234 said:
1. Find all real solutions: (dx/dt)-2x=cos(3t)



2. Homework Equations



3. I really don't know where to start here. Any advice to get me on my feet would be appreciated.
Try to find an integrating factor.
 
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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