Question: Find a differential equation whose general solution is $y = c_1e^{2t}+c_2e^{-3t}$
Since the solution is the linear combination of $y_1=e^{2t}$ and $y_2=e^{-3t}$
So,consider $r_1=2$ and $r_2=-3$ such that $(r-2)(r+3)=0$
So, $r^2+r-6=0$
Therefore, we know the equation $y''+y'-6y=0$ satisfies our solution
