Chapter 3 - Second Order Linear Equations - 3.2 Solutions of Linear Homogenous Equations; the Wronskian - Problems - Page 155: 1

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

$W(e^{2t},e^{-\frac{3t}{2}}) = |\begin{matrix} e^{2t} & e^{-\frac{3t}{2}}\\ 2e^{2t} & -\frac{3t}{2}e^{\frac{-3t}{2}}\\ \end{matrix}| = -\frac{3e^{\frac{t}{2}}}{2}-2e^{\frac{t}{2}}=-\frac{7}{2}e^{\frac{t}{2}}$