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