The pond initially has 1000000 gal of water and the unknown amount of the undesirable chemical. Water having 0.01 g of this chemical per gallon flows into pond at the rate of 300 gal . Mixture flows out at same rate such that amount of water in pond remains constant. Suppose that chemical is uniformly distributed throughout pond at any time.

i) Derive the ordinary differential equation describing amount of chemical over time.

ii) Compute order of differential equation derived in part a).

iii) Is differential equation derived in part i) linear or nonlinear? Prove the statement.

iv) Determine general solution of differential equation derived in part i).

v) New information reveal that, at time t = 0, there have been 5 kg of chemical in pond. Derive the initial value problem describing amount of chemical over time.

vi) Solve initial value problem derived in part v).