Chapter 16.2, Problem 71E

Wronskian The Wronskian of two differentiable functions f and g, denoted by W (f, g), is defined as the function given $W(f,g)=\left|\begin{array}{cc}f& g\\ f\text{'}& g\text{'}\end{array}\right|$.

The function f and g are linearly independent when there exists at least one value of x for which $W(f,g)\ne 0$. In exercise 71-74, use the Wronskian to verify that the two functions are linearly independent.

$\begin{array}{l}{y}_1=e^{ax}\\ y_2=e^{bx},a\ne b\end{array}$