Consider the first order differential equation

y′+(t/t^2−4).y=e^t/(t−5)

For each of the initial conditions below, determine the largest interval a< t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.

a. y(-7)=6.4
b. y(2.5)=-0.5
c. y(0)= 0
d. y(4.5)= -2.1
e. y(14)= 1.7