- #1

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x'' = 2x' + x = 3cos2t + sin2t

My understanding is that I need to find the general solution for the unforced equation and a particular solution of the above equation. When these are added together then I will get my final solution.

Using the charateristic equation:

m^2 + 2m + 1 = 0

And then the quadratic equation will give me:

m = -1

This gives a general solution of:

x(t) = Ae^m0t + Bte^m0t

so

Ae^-1t + Bte^-1t + particular solution = final answer

Is a particular solution

x(t) = p cos βt + q sin βt....???

Not really sure where to go from here.