how to solve ODE that contains integration over time?

Hi,

I need to solve the attached ODE. I known how to handle with X as a matrix. My problem is the integral. How can I plug it inside the ODE45 solver? Is it possible on Matlab?

Thank you!

Answer 1

[Bjorn Gustavsson]

For this type of integro-differential equations the standard "first-stab" trick is to differentiate it one step, which should give you the second-derivative of X on the LHS and something you can work out analytically for the RHS such that the integral will vanish when taking the limit of the RHS derivative. Then you'll have a system of second-order ODEs.

HTH