For the RL series circuit shown below, the current 1(t) in the circuit satisfies ODE: L L + RI = V R (a) Solve the equation for I(t), assuming that R, L, V are all constants. You may treat the equation as either linear or separable. (b) Find the solution satisfying the initial condition: (0) = 1. (c) Evaluate lim[1(t)]. 2. A large cylindrical tank initially contains 100 gallons of pure milk. At t=0 min. chocolate milk containing 40 grams of chocolate/gallon is poured into the tank at the rate of 3 gallons per minute, and the mixture is pumped out of the tank at the rate of 2 gallons per minute. bratar Outlet (a) Set up and solve the ODE for A (t), the amount (measured in grams) of chocolate in the tank at time t. HINT: The equation is linear, and the integrating factor is (t)= (100+t). (b) Determine the particular solution satisfying the initial condition: A (0) = 0.