Problems

In Problems 1-4, find the general solution of the given differential equation.

In Problems 5-12, find the particular solution of the initial value problem.

15            A function y(t) is a solution of the differential equation y' + ky = 0 for some constant k. Given that y(0) = 100, and y(2) = 4, find k and find y as a function of t.

16            A function y(t) is a solution of the differential equation y' + t^k y = 0 for some constant k. Given that y(0) = 1,and y(1) = e^-1/3, find k and find y as a function of t.

17            A bacterial culture grows at a rate proportional to its population. If it has a population of one million at time t = 0 hours and 1.5 million at time t = 1 hour, find its population as a function of t.

18           A radioactive element decays with a half-life of 6 years. Starting with 10 lb of the element

at time t = 0 years, find the amount of the element as a function of t.