## anonymous 5 years ago Find the value(s) of m such that y = e^(mx) is a solution to the differential equation: y'' -8y' +15y = 0

1. anonymous

Use the Characteristic equation to find the values of m, by finding the roots of the CE

2. anonymous

m=3 or 5

3. anonymous

4. anonymous

The Characteristic equation is is$m^2-8m+15\rightarrow (m-5)(m-3)\rightarrow m=3,m=5$ the solution is: $y=C_{1}e^{3x}+C_2e^{5x}$

5. anonymous

thanks i just got stuck at this point $m ^{2}−8m+15$ i had $m ^{2}y−8my+15y$ nd completely forgot about the CE equation thanks!

6. anonymous

no problem