Question

Laplace transformation differential equation: solve IVP: y''-y=-20delta(t-3); y(0)=1, y'(0)=0. I got the basic laplace transformation but am unsure about the partial fractions and converting back via inverse laplace. i have the answer but need to show my work and my work is wrong.

Answer 1

http://tutorial.math.lamar.edu/Classes/DE/InverseTransforms.aspx might help

Answer 2

that's what I was working off of and I solved for Y=(-20e^(-3s)+s-1)/(s^2-s). The correct final answer is cosh(t)-20u(sub3)(t)sinh(t-3). which means my Y should be in teh form s/(s^2-a^2) in order for the inverse laplace to be cosh(t). and I should have a form a/(s^2-a^2) with the heavyset term to use the inverse laplace sinh(t-3). I don't have either of these forms.

Answer 3

hi is the delta might be the U? in the unit step function?