Consider the initial value problem: y' - (7/2)y = 7t + 2e^t
Initial condition: y(0) = y0
a) Find the value of y0 that separates solutions that grow positively as t → [infinity] from those that grow negatively. (A computer algebra system is recommended. Round your answer to three decimal places.)
b) How does the solution that corresponds to this critical value of y0 behave as t → [infinity]?
Will the corresponding solution increase without bound, decrease without bound, converge to the function y = 0, converge to the function y = -7t, or converge to the function y = 7t?