Q1: a) Verify that the given two-parameter family of functions is the general solution of the differential equation. b) Find a member of the family that is a solution of the initial value problem. y = ce^x + Ce^-x; y' - y = 0, y(0) = 0, y'(0) = 1
Q2: Determine whether the given set of functions is linearly independent:
1. f1(x) = e^x
2. f2(x) = e^x
3. f3(x) = x
4. f4(x) = x^2
5. f5(x) = 4x - 3x^2