Find the Wronskian?

Question

Find the Wronskian of e^2t, e^(-3t/2).

W(f, g)=fg'-gf'

-3/2e^2t(e^-3t/2)-e^(-3t/2)(2e^2t)

=-3/2e^(7t/2)-2e^t/2.

Am I right?

Answer 1

You were on the right way. Your answer is  -(7/2)e ^t/2.

Check. If f (t) = e ^2t, and g(t) = e ^-3t/2, then f'(t) = 2e ^2t, g'(t) = (-3/2) e ^-3t/2. Thus,

  Det W(f.g) = fg' - gf' = -3/2 e ^t/2 - 2 e ^t/2 = -7/2 e ^t/2. .