Hello everyone i'm lost on how they want me to approach this:(adsbygoogle = window.adsbygoogle || []).push({});

Find the two values of k for which

y(x) = e^{kx}

is a solution of the differential equation

y'' - 16 y' + 60 y = 0.

smaller value =?

larger value = ?

I did the following:

y(x) = e^(kx);

y' = ke^(kx);

y'' = k^2e^(kx);

(k^2e^(kx)) - 16(ke^(kx)) + 60(e^(kx)) = 0;

is there a sysematic way to solve this problem rather then just trying to randomly guess numbers? i tried the randomly guessing k values and it isn't working out

Any help would be great!

thanks!

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# Diff Eq problem, finding the small value and large value of k?

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