Is this differential equation involving an integral solvable by Matlab?

Is the following equation solvable by Matlab:

initial conditions are F = 0, y = 0, dy/dt = 0. Otherwise, do I have to solve step by step? As in, I take F=0 for t=1 and then find the corresponding values for y and dy/dt and then take those y and dy/dt values to find F at time t=2 and then use F to find y etc.?. This is to solve the self-excited forces F of a structure due to wind at different times t so F is a variable. I would really appreciate any input as this is really important and I'm getting desperate. Thank you!

[darova]

Is there any connection between F and y or dy?

[Saruultugs Batzorig]

They are both just functions of t. y is the displacement and F the resultant force.

[darova]

There must be an additional condition between y and F

Where is this equation from?

[Saruultugs Batzorig]

Apparently it can be solved using a finite difference method. It's from a paper.

Answer 1

[Nadir Altinbas]

part part solve derivates and integration separately then combine into differintial