How to plot and solve the numerical solution of a integro-differential equation

I have a integro-differential equation of the form 
$y'(t) =  - \int_0^t {y(t_1 )} f(t - t_1 )dt_1 . t \in [0,15], y(0) =
1$. The function f(t - t_1 ) depends (in a complex way) on t and t_1, here assuming f(t - t_1 )=\frac{1}{{(1 + t-t_1)^4 }}.

[Freyja]

Hey there, did you ever solve this? I have a very similar project and would be interested in whether you managed to program it. Best regards, Freyja