Given solutions  and  to the systemwe define the Wronskian of Y1(t) and Y2(t) to be the (s...

Given solutions  and  to the system

we define the Wronskian of Y1(t) and Y2(t) to be the (scalar) function

(a) Compute dW/dt.

(b) Use the fact that Y1(t) and Y2(t) are solutions of the linear system to show that

(c) Find the general solution of the differential equation

(d) Suppose that Y1(t) and Y2(t) are solutions to the system dY/dt = AY. Verify that if Y1(0) and Y2(0) are linearly independent, then Y1(t) and Y2(t) are also linearly independent for every t.