Question

A salt tank contains 100 liters of pure water at time t= 0, when salty water begins flowing into tank at 2 liters per second. The incoming liquid contains 1/2 kg of salt per liter. The well-stirred liquid flows flows out of the tank at 2 liters per second.
1) Model the situation with a first order DE, and find the amount of salt in the tank at any time.
2) Suppose that the at time t = 20 seconds 5 kg of salt is instantaneously dumped into the tank. Modify the DE from the previous part (hint: a delta function appears on the right side). Solve the resulting DE using laplace transform. Plot the s

Answer 1

I find it really hard to believe you know Laplace transformations and can't set up part 1. If you're really stuck on setting up mixing problems, watch this:
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-3-solving-first-order-linear-odes/

Answer 2

And for the record, here is an example of solving an ODE with a dirac-delta function, using Laplace transformations. (beginning at around 20:00):
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-23-use-with-impulse-inputs/