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Math Help - Non-Homogeneous DQ's

  1. #1
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    Non-Homogeneous DQ's

    Hello, I am having some trouble with these second and third order non-homogeneous dq's.

    I can identify a Y compliment, but I freeze up when I have to distinguish the Y particular.

    ex 1) Solve:

    y'' - y' = 11x + 1

    Ycompliment -

    (D^2 - D)y = 0
    D(D-1)y = 0

    Roots: D= 0, 1

    Yc = c1 *e^0x + c2 *e^x = 1 + c2 *e^x

    Now this is where I get lost... I can ID Yc but not Yp. Please help! Thanks!
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  2. #2
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    For the particular integral try y = ax^2 + bx

    Bobak
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  3. #3
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    Thanks for the help!

    One question, how do you arrive at this solution? If you could explain further, the process, I would greatly appreciate it!

    I understand that it's more of a guessing thing, but how should I make the best guess?

    Thanks again, Chris
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  4. #4
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    Quote Originally Posted by ccdelia7 View Post
    Thanks for the help!

    One question, how do you arrive at this solution? If you could explain further, the process, I would greatly appreciate it!

    I understand that it's more of a guessing thing, but how should I make the best guess?

    Thanks again, Chris
    It is not guessing at all. From the differential equation it should be obvious that the particular integral is a polynomial, in which case all you need to determine is the order of the polynomial, Can you explain why such a polynomail for this differential equation must have a zero ceofficient on any terms higher than x^2?

    Bobak
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  5. #5
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    Quote Originally Posted by bobak View Post
    For the particular integral try y = ax^2 + bx

    Bobak
    Actually you can get away with y = ax^2 + bx + c

    -Dan
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  6. #6
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    Quote Originally Posted by topsquark View Post
    Actually you can get away with y = ax^2 + bx + c

    -Dan
    No point there is a constant term in the complementary solution.

    Bobak
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