a) Find the general solution to the homogeneous differential equation.

d2y/dx2 + 4dy/dx -5y = 0

in your answer to denote arbitrary constants, and enter them as c1 and c2. y(x) = ?

b) Find the solution to the boundary value problem:

d2y/dx2 -9dy/dx +18y = 0, y(0) = 8 , y(1) = 5

y= ?

c) Consider the initial value problem

d2y/dx2 - 3dy/dt -4y = 0 , y(0) = a , y'(0) = -10

1) Find the solution of the initial value problem:

y(t) = ?

2) Find a so that the solution approaches zero as t -> inf .

a = ?