Question

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

Answer 1

The given pair of functions is
$u_{1}(t) =e^{2t}, \, u_{2}(t)=e^{- \frac{3t}{2}}$

The derivatives are
$u_{1}{'}=2e^{2t} \\ u_{2}^{'} = - \frac{3}{2} e^{- \frac{3t}{2} }$

The Wronskian is
$W=\begin{pmatrix} e^{2t} & e^{- \frac{3t}{2}}\\2e^{2t} & - \frac{3}{2}e^{- \frac{3t}{2}} \end{pmatrix}=- \frac{3}{2}e^{t/2}-2e^{t/2}=- \frac{7}{2}e^{t/2}$

Answer: $- \frac{7}{2}e^{ \frac{t}{2}}$