Consider the differential equation

$y^{\text{'}\text{'}}-y^{\text{'}}-6y=0$

Verify that the functions $e^{-2x}$ and $e^{3x}$ form a fundamental set of solutions of the differential equation on the interval $(-,$ in$).$

The functions satisfy the differential equation and are linearly independent since the Wronskian $w(e^{-2x},e^{3x})=x,0$ for $-,$