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Math Help - Solve for y...

  1. #1
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    Solve for y...

    I'm doing differential equations and got stuck on this part.

    How do I solve for y if I have the equation:

    -siny = x^2 + C

    Thanks
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  2. #2
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    Quote Originally Posted by jzellt View Post
    I'm doing differential equations and got stuck on this part.

    How do I solve for y if I have the equation:

    -siny = x^2 + C

    Thanks
    -\sin y = x^2 + C

    \sin y = C-x^2

     y = \sin^{-1}(C-x^2)
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  3. #3
    Senior Member Educated's Avatar
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    Quote Originally Posted by pickslides View Post

     y = \sin^{-1}(C-x^2)
    Shouldn't it be minus c as well?

    Here's what I got:

    -\sin y = x^2 + C

    \sin y = -C-x^2

    y = \sin^{-1}(-C-x^2)

    OR

    y = -\sin^{-1}(C+x^2)
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  4. #4
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    Quote Originally Posted by Educated View Post
    Shouldn't it be minus c as well?
    Its a constant \displaystyle c\in \mathbb{R} , why should it be negative?
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  5. #5
    Senior Member Educated's Avatar
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    Maybe this is why I'm still in high school.

    Just ignore me then... I haven't learnt those things yet.


    EDIT:

    Wait...

    \displaystyle c\in \mathbb{R}

    c is and element of a real number...

    Isn't -c a real number? Why isn't -c allowed?
    Last edited by Educated; September 13th 2010 at 10:12 PM. Reason: Real numbers question
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  6. #6
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    Quote Originally Posted by Educated View Post

    c is and element of a real number...
    Therefore can be positive or negative.
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  7. #7
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    Since C is an arbitrary real number, it doesn't matter whether C is positive or negative and it doesn't matter whether we call it "C" or "- C". The same thing happens often with exponentials. If you have a solution to an equation of the form e^{x+ C} where C is an arbitrary constant, you can write that as e^{x+ C}= e^C e^x or simply as C e^x. Strictly speaking, we should use a different symbol, say C' with the explanation that C'= e^C but typically, knowing that they are both just arbitrary numbers, that is not done.
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