Find the values of the parameter r for which the function y

Find the values of the parameter r for which the function y = e^rx is a solution of the equation y\" - 11y\' + 30 y = 0.

We substitute y=e^{rx} and get

r^2-11r+30=0

r^2-5r-6r+30=0

r(r-5)-6(r-5)=0

(r-5)(r-6)=0

r=5,6

So for r=5 and 6 y=e^{rx} is solution to given equation.

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