- #1
ollyfinn
- 14
- 0
I am trying to solve the following problem and am a bit lost so any advice would be welcomed.
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.
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.