bio calc differential equation webwork

Question

1)

Let y''-4y = 0.

Find all values of r such that y=ke^(rx) satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list. 

2)

which of the following functions are solutions to the differential equation y''-9y'+18y=0

a.) y(x)=0

b.) y(x)=6x

c.) y(x)=3x

d.) y(x)=e^(x)

e.) y(x)=e^(6x)

f.) y(x)=e^(-x)

g.) y(x)=e^(3x)

I got E and G when I did this problem on my own but got the problem wrong when I submitted it.

Answer 1

hi Sara,

y = k e^rx

y' = k r e^rx

y" = k r² e^rx

y" - 4 y = 0 ------> kr²e^rx - 4 k e^rx = 0 ------> k e^rx ( r² - 4 ) = 0 ----->. r² - 4 = 0 r = ±2

you are right, correct answers are e, g and a that you forgot.

I hope it is useful,

Minoo