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 [tex]\frac{dw}{dt} = k*t*w, w(0)=30[/tex] as initial condition.