Question

Find the wronskian of the given pair of functions. 1. e2t, e−3t/2

Answer 1

The given pair of functions is

`u_(1)(t) =e^(2t), \, u_(2)(t)=e^{- (3t)/(2)}`

The derivatives are

`u_(1){'}=2e^(2t) \\ u_(2)^(') = - (3)/(2) e^{- (3t)/(2) }`

The Wronskian is

`W=\begin{pmatrix} e^(2t) & e^{- (3t)/(2)}\\2e^(2t) & - (3)/(2)e^{- (3t)/(2)} \end{pmatrix}=- (3)/(2)e^(t/2)-2e^(t/2)=- (7)/(2)e^(t/2)`

Answer:
`- (7)/(2)e^{ (t)/(2)}`