Question

For what values of r does the function y = 6e^(rx) satsify the differential equation y'' - y' - 42y = 0

Answer 1

Compute the first derivative like this:

`(6e^(rx))'=6re^(rx)`
Second derivative:

`(6re^(rx))'=6r^2e^(rx)`
From the given equation we get:

`6r^2e^(rx)-6re^(rx)-42*6e^(rx)=0`
Simplify like this:

`6r^2-6r-252=0`
Solving the above equation for r we get:
r=-6 or r=7