Chapter 4 - Vector Spaces - 4.8 Applications of Vector Spaces - 4.8 Exercises - Page 219: 15

$$W=-2 \mathrm{e}^{x} \mathrm{e}^{-x}$$

The Wronskian of $\left\{e^{x}, e^{-x}\right\}$ is given by $$W=\left|\begin{array}{cc}{e^{x}} & {e^{-x}} \\ {e^{x}} & {-e^{-x}}\end{array}\right|=-2 \mathrm{e}^{x} \mathrm{e}^{-x}$$