Inverse Laplace for a something in sin form but with an addition power of two on the bottom

by user3186491   Last Updated November 13, 2017 00:20 AM

I have a question asking to solve the following with Laplace transformations. I get through most of it, but I'm stumped in the final stage.

y"+4y'+29y=e^(-2t)sin(5t) y(0)=5, y'(0)=-2

I run through the whole thing until I end up here.

Y(s^2+4s+29)=5s+3+(5/((s+2)^2+25))

I can divide and solve for the 5s+3 bit fine, but the issue is that the part in the very right, the laplace transformation of e^(-2t) sin(5t), gains a power of two on the bottom, as s^2+4s+29 becomes (s+2)^2+25. I have no idea how to inverse Laplace from that.



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