How would you solve this?
I did the standard way of solving questions like these - I took the Laplace of both sides and used the convolution identity. But the solution I got, $f(t)=3+t^2/2$, does not satisfy the integral equation, nor does it satisfy the initial conditions. I have a feeling that the derivative includes the Dirac delta function, but I'm not really sure how to find this. Any help will be much appreciated. Here is my working out. enter image description here
