# Thread: Simple "For what value of r does it satisfy..."

1. ## Simple "For what value of r does it satisfy..."

We sort of blew through this chapter, so I'm not sure how to do this:

For what values of r does the function $\displaystyle y=e^{rx}$ satisfy the differential equation $\displaystyle 6y'' + 11y' - 2y = 0$?

Would I literally just derive it and solve for r? Seems really messy.

2. Originally Posted by Open that Hampster!
We sort of blew through this chapter, so I'm not sure how to do this:

For what values of r does the function $\displaystyle y=e^{rx}$ satisfy the differential equation $\displaystyle 6y'' + 11y' - 2y = 0$?

Would I literally just derive it and solve for r? Seems really messy.
Literally take the derivatives and substitute

$\displaystyle (6r^2 + 11 r-2)e^{rx} = 0$
and solve the quadratic equation for $\displaystyle r.$

3. That gave me the answer but...

Why did you just replace y' with r and move the function to the outside?

4. He didn't. With $\displaystyle y= e^r$, $\displaystyle y'= re^r$. He replaced y' with that and factored $\displaystyle e^r$ out.