## 2nd order Linear DE

Hi,

When solving a 2nd order Linear DE with constant coefficients ($ay''+by'+cy=0$) we are told to look for solutions of the form $y=e^{rt}$ and then the solution (if we have 2 distinct roots of the characteristic) is given by
$y(t)=c_1 e^{r_1 t}+c_2 e^{r_2 t}$

This is clearly a solution, but how do we know there are no other solutions?
That is, how do we know this is the general solution?
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