Question

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

Answer 1

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

Answer 2

m=3 or 5

Answer 3

thanks, what was your working?

Answer 4

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

Answer 5

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!

Answer 6

no problem