Solve the following Laplace Transform:
x````(t) + x```(t) = sint where: x(0)=x`(0)=x```(0) = 0 and x``(0)=2
I believe I manipulated it correctly to the following:
X(s) = 1/(s^4+s^3)(s^2+1) + 2/s^3
Now I do not know how to manipulate this using partial fractions method. The denominator of the 1st RHS term is confusing me. Is there anyone that could help?
Now going back into the time domain I would get
(-t)+(3t^2)-(.5e^-t) +(?) I know this is someway to algebraically manipulate the last term, but im 3 semesters out of my Diff EQ class and forgot how. Is there anyway you could explain what to do?
Edit: can I do s/s^2+1 + 1/s^2+1 to get
(-t) + (3t^2) - (.5e^-t) + (.5sint) +(.5cost)
Okay, I understand that above. I have one last question, I'm working on another problem and I get my equation in the s domain to be the following:
How would I go about algebraically manipulating the second part of the RHS to get it back into the time domain?