Hey guys, I had the following problem on an exam and it stumped me pretty good.  

I get V(t) = 20 + 2t and the tank is full at t = 30 minutes

Next, C(t) = x / V(t) or C(t) = x / (20 + 2t)

Part d, writing the ODE, is where I got stumped.  There is 0 lb of salt initially, 3/2 lb of salt entering the tank each minute, and x / (20 + 2t).  Does that mean dx/dt = (3/2)t - x / (20 + t)?  For some reason that doesn't seem correct.

Of course, x(0) = 0 and I didn't get around to part f  or beyond because I didn't think I had the ODE right so I moved onto other problems and then ran out of time.  That said, to solve I would write is as a first order linear ODE and use the integrating factor, correct?

Here is the full problem: