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Math Help - Answer to exam question correct?

  1. #1
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    Question Answer to exam question correct?

    Hi ,

    i'm a first year student in biology from Brussels and, as most students do, have passed a math exam today. I'm not quite sure whether my solution to one of the questions is correct. I was wondering if somebody could check/confirm my answer? thx a lot ^^

    The 2nd degree linear non homogenic DE is as follows :

    y'' - 2y' - 3y = e^(-x)

    Using the method of variation of parameters to find the particular solution Yp I found this general solution

    Y = Yc + Yp = c1 e^(3x) + c2 e^(-x) – e^(-x)* ((1 + 4x) / 16)


    Is this correct? I'm also wondering if I should have used the method of undetermined coefficients instead?
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  2. #2
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    Quote Originally Posted by pnklv View Post
    Hi ,

    i'm a first year student in biology from Brussels and, as most students do, have passed a math exam today. I'm not quite sure whether my solution to one of the questions is correct. I was wondering if somebody could check/confirm my answer? thx a lot ^^

    The 2nd degree linear non homogenic DE is as follows :

    y'' - 2y' - 3y = e^(-x)

    Using the method of variation of parameters to find the particular solution Yp I found this general solution

    Y = Yc + Yp = c1 e^(3x) + c2 e^(-x) e^(-x)* ((1 + 4x) / 16)


    Is this correct? I'm also wondering if I should have used the method of undetermined coefficients instead?

    Remember you can always check by plugging the solution into the ODE.

    According to maple your solution checks and personally I would have used undetermined coefficeints but either way is correct.

    Answer to exam question correct?-ode.jpg
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    Remember you can always check by plugging the solution into the ODE.

    According to maple your solution checks and personally I would have used undetermined coefficeints but either way is correct.

    Click image for larger version. 

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    Thanks 4 check, life saver since the triple integral on my exam near dragged my points down below 12/20

    Srry if this seems a stupid question, but what is ODE ( i assume a program/applet to calc DE's) & where can I find it ? ( might come in handy later )
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  4. #4
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    Quote Originally Posted by pnklv View Post
    Thanks 4 check, life saver since the triple integral on my exam near dragged my points down below 12/20

    Srry if this seems a stupid question, but what is ODE ( i assume a program/applet to calc DE's) & where can I find it ? ( might come in handy later )
    ODE means Ordinary differential equation.

    What I ment is you cant take derivatives of your solution and plug them into the ode and check your solution. This is exactly like solving

    2x+4=0 \implies x=2

    and plugging x=2 into it to check your solution.

    IF you look at the attached immage above this code

    Code:
      diff(y,x$2)-2*diff(y,x)-3*y
    means

    y''-2y'-3y
    and it did give the correct solution.
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