Question

Let's have some (Monday) fun!

I will give free medals for those who at least try to solve the following, not-so-bad differential equation:\[f(t)+2\int_{0}^{t}f(\tau)\cos(t-\tau)d\tau=4e^{-t}+\sin t.\]Have fun! :)

Answer 1

will solve step-by-step upon request...

Answer 2

my guess would be to rewrite the integral as a convolution and use laplace transforms. can you take a look at my question? :))

Answer 3

That's correct. :)