Josephood7

Find the general solution to the differential eauation [math] Assume [math], and use C (capital C) for your arbitrary constant.

Find the particular solution of the differential equation [math] satisfying the initial condition [math].
Answer: [math]= 
Your answer should be a function of [math].

Solve the initial value problem [math].

[math] 

 Find the general solution to

[math]
Enter your answer as [math] .
Use [math] to denote the arbitrary constant in your answer.

A tank contains [math] kg of salt and [math] L of water. Water containing [math] of salt enters the tank at the rate [math] [math]. The solution is mixed and drains from the tank at the rate [math] [math]. A(t) is the amount of salt in the tank at time t measured in kilograms.

(a) A(0) =  (kg)

(b) A differential equation for the amount of salt in the tank is  [math]. (Use t,A, A', A'', for your variables, not A(t), and move everything to the left hand side.)
(c) The integrating factor is 
(d) A(t) =  (kg)

(e) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)