Thread: Another Dif EQ Prob

Find all values of m such that the function below is a sol'n of the given Diff. Eq. Explain why this is true.

y'' - 5y' + 6y = 0; y = e^(mt)

$\displaystyle y=e^{mt}$
$\displaystyle y'=me^{mt}$
$\displaystyle y''=m^2e^{mt}$
Plug in the equation and we get $\displaystyle e^{mt}(m^2-5m+6)=0$
So, you have to solve a quadratic equation: $\displaystyle m^2-5m+6=0$