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Math Help - 4th order differential equation??

  1. #1
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    Question 4th order differential equation??

    d4y/dx4 - 8( d2y/dx2) + 16y = 0

    This is on one of my '2nd order differential equations' problem sheets and its a of fourth order leaving me a bit confused. Ive tried reducing the order but I cant get it. Is there a rule/theorem Ive missed??

    A helping hand would be greatly appreciated

    Nappy
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  2. #2
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    Why do you need to reduce it?

    1) Create a system z = d2y/dx2. What does that do after some substitution?

    2) Factor the characteristic polynomial in ignorance ==> I didn't even notice it wasn't second degree! Just see what happens.
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  3. #3
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    Yea I tried that method and it was fine for the first 2 terms but I didnt know what to do with the 16y term, integrating twice seems a bit messy??

    so i get

    z'' -8z + 16y= 0

    How to convert the y value??
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  4. #4
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    Did you factor the Characteristic Polynomial? That's a great place to start.
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