I'm working on a engineering problem and I need to solve this nasty differential. I gave it a go with Laplace transforms, but no luck. Any ideas? Note: a, b, c, and k are constants.
$$\frac{dm(t)}{dt}=\frac{a-b\cdot m(t)}{c\cdot t-\int_{t_i}^t m(x)\,dx}-k\cdot m(t)$$