I am trying to solve
using Laplace transforms.
I end up with
where H(t-a) is the Heaviside/unit step function. Is this correct? If not, where have I gone wrong?
Hmm. That isn't what I get. You're missing the complimentary function, I think.
1. How can you write the original DE in one equation using the Heaviside step function?
2. What do you get when you LT the DE?
3. What are the initial conditions?
4. So what do you get when you solve for the LT of y?