How do I solve a dr/dt equation?

I just need an example of how to solve basic integrals to get the r's at different timesteps. I have an equation:

How do I solve it at t=0 for example, if it has r's on both sides?

[Roger Stafford]

What you have there is a differential equation, which is different from a problem in integration. In matlab these can be solved numerically using one of the ‘ode’ functions (ordinary differential equations.) See for example:

   http://www.mathworks.com/help/matlab/ref/ode45.html

You will need to furnish an initial value for ri.