AboutDr. Nyayapati Swami Expertise I can help you in solving first and second order differential equations. Questions must be at the Undergraduate level. Do not expect me to do all your homework.. If you have a homework question with no clues on how to go about, I will only give you some pointers on solving them.
Experience Ph.D. in Mathematics with more than 15 years of teaching. In addition to undergraduate calculus, I taught many more advanced subjects like Complex Analysis, General Topology, Numerical Analysis, Operations Research, Graph Theory, Mathematical Analysis, Mathematical Economics, Optimisation Theory.
Education/Credentials Ph.D. (University of Toledo, USA)
A 200 gal tank is half full of distilled water. At time t = 0 a solution containing o.5 lb/gal of concentrate enters the tank at the rate of 5 gal/min, and the well-stirred mixture is withdrawn at the rate of 3 gal/min.
a) At what time will the tank be full?
b) At the time the tank is full how many pounds of concentrate will it contain?
Answer a) The tank will be full in 50min
[Water enters at 5gal/min and withdrawn at 3gal/min, so the net increase is 2gal/min. Therefore for 100gal increase it will take 100/2=50min]
b) At time t, the amount of water in the tank is 100 + 2t (because it increases at 2gal/min).
Suppose C(t) is the amount (in pounds) of concentrate at time t.
The amount of concentrate in 3gal is 3C(t)/(100 + 2t)
The equation for C(t) is therefore
dC/dt = 0.5(5) - 3C(t)/(100 + 2t)
This is a first order linear equation in C:
dC/dt + 3C(t)/(100 + 2t) = 2.5
Excercise: Solve this equation with the initial condition C(0) = 0 and then compute C(100).
