For what values of $r$ does $y=e^{rx}$ satisfy $y'' + 5y' - 6y = 0$? For what values of $r$ does $y=e^{rx}$ satisfy $y'' + 5y' - 6y = 0$?
Attempt:
$y' = [e^{rx}] (r)$
$y''= r^2e^{rx}$

If you plug them in, you obtain : $$r^2+5r-6=0$$
Solving this equation you get $r=1$ or $r=-6$.
That means that the general solution of the suggested ODE is : $$y(x)=ae^t + be^{-6t}, (a,b) \in \Bbb R^2$$
