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  1. #1
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    Solve

    Solve

    x'+y=t
    y'-x=-t

    I am confused, and need some guidence!
    Please and Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mandy123 View Post
    Solve

    x'+y=t
    y'-x=-t

    I am confused, and need some guidence!
    Please and Thanks
    Differentiate the first again:

    x''+y'=1

    so, substituting the second into the first:

    x''+x=t+1

    and for y you can differentiate the second and substitute the first.

    CB
    Last edited by CaptainBlack; April 7th 2009 at 07:53 PM. Reason: corrected the typo
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  3. #3
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    ok, but shouldn't it be

    x'' + x = 1 + t

    and then

    y'' + y = t - 1

    what happened to the 1 in your first equation?
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  4. #4
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    Quote Originally Posted by mandy123 View Post
    ok, but shouldn't it be

    x'' + x = 1 + t Mr F says: Yes. CB made a small mistake (he makes one every year). But it's the method that's important.

    and then

    y'' + y = t - 1

    what happened to the 1 in your first equation?
    Your equations are correct and there should be no problem solving them.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by mandy123 View Post
    ok, but shouldn't it be

    x'' + x = 1 + t

    and then

    y'' + y = t - 1

    what happened to the 1 in your first equation?
    Typo now corrected.

    CB
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  6. #6
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    so would my answer of

    x(t)=Acos(t) + Bsin(t) + 1 + t
    y(t)=Acos(t) + Bsin(t) - 1 + t

    be the right answer, or did i mess up somehow?
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  7. #7
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    Quote Originally Posted by mandy123 View Post
    so would my answer of

    x(t)=Acos(t) + Bsin(t) + 1 + t
    y(t)=Acos(t) + Bsin(t) - 1 + t

    be the right answer, or did i mess up somehow?
    Do they work when you substitute them into the given pair of differential equations?
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