Acolony of 200 weasels on a remote island are suffering from a new disease. let w(t) be the number of sick weasels at time t. suppose that 30 weasels are sick initially and the disease is spreading at a rate proportional to the product of the time elapsed and the square root of the number of sick weasels. give the mathematical model (ivp) for w.

Given that w(t) is the number of sick weasels at time t.

And there are 30 sick weasels initially.

That is at t=0, w is 30. Else we can write that as w(0)=30.

And also given that disease is spreading at a rate proportional to product of time elapsed and square root of the number of sick weasels.

That is dw/dt is proportional to t*w.

Let k be the proportionality constant.

Hence differential equation is as initial condition.