Differential Equations?

Question

Sorry to ask another one, but this Calc class is killing me. So my question is:
Find the two values of k for which y(x) = e^kx
is a solution of the differential equation y"-17y' + 72y= 0.

I need to find the two values but I keep getting the wrong answers. Thank you for your help :)

Answer 1

Hi,
The characteristic equation is this:
r²-17r +72=0
(r-9)(r-8)=0
r-9=0
r=9
r-8=0
r=8
Then,
y=c1e^(9x) +c2e^(8x)
Where the constants are determined by the initial conditions.

FE