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Math Help - Simple "For what value of r does it satisfy..."

  1. #1
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    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 y=e^{rx} satisfy the differential equation 6y'' + 11y' - 2y = 0?

    Would I literally just derive it and solve for r? Seems really messy.
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  2. #2
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    Quote Originally Posted by Open that Hampster! View Post
    We sort of blew through this chapter, so I'm not sure how to do this:

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

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

     <br />
(6r^2 + 11 r-2)e^{rx} = 0 <br />
    and solve the quadratic equation for r.
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  3. #3
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    That gave me the answer but...

    Why did you just replace y' with r and move the function to the outside?
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  4. #4
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    He didn't. With y= e^r, y'= re^r. He replaced y' with that and factored e^r out.
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