Question

For what values of r does the function y= e^rx satisfy the differential equation 2y"+y'-y=0?

Answer 1

do the same thing..

Answer 2

If r1 and r2 are the values of r that you found in part (a), show that every member of the family of functions =ae^r1x+be^r2x is also a function

Answer 3

Like I said earlier, my deriving processing is not up to speed yet, Im just trying to get a few questions out so I can learn from understanding the process first

Answer 4

y = e^(rx)
y' = re^(rx)
y'' = r^2e^(rx)

Answer 5

2y'' + y' - y = 0
2r^2 e^(rx) + r e^(rx) + e^(rx) =0

Answer 6

wait sorry that should be a minus

Answer 7

2y'' + y' - y = 0
2r^2 e^(rx) + r e^(rx) - e^(rx) =0

Answer 8

Divide everything by e^(rx)
2r^2 + r - 1 = 0

Answer 9

r = -1, r = 1/2

Answer 10

your good haha, mathematics major?

Answer 11

yea

Answer 12

now for the next part:
now for the next part:
y=ae^r1x+be^r2x
y = ae^(-x) + be^(x/2)

Answer 13

y' = -ae^(-x) + (b/2)e^(x/2)
y'' = ae^(-x) + (b/4)e^(x/2)

Answer 14

hold up let me write this out on paper, im getting confused..

Answer 15

so you're going to hate me for this comment but from 2r^2 + r - 1 = 0, did you use the quadratic or did you factor?

Answer 16

I used wolframalpha haha.. and I always use quadratics, I can't factor lol never learned that properly so I don't hate you..
I used http://www.wolframalpha.com/input/?i=Solve%282r%5E2+%2B+r+-+1+%3D+0%29

Answer 17

heh yess wolfram is a Godsend. Im an atmospheric science major

Answer 18

still working on the second part?>

Answer 19

Here you go, I get confused if I type, i have to see it on paper..

Answer 20

thank you

Answer 21

np