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Math Help - [SOLVED] Please solve this...

  1. #1
    Member Altair's Avatar
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    [SOLVED] Please solve this...

    Form the differential equation :-

    'v = f( x - by) + g( x + by), where f and g are twice differentiable'.

    What hint does the statement 'where f and g are twice differentiable' give us?

    And the answer is in the form of Partial Derivatives. How do I know where to use Ordinary derivative and where to use the Partial Derivative?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Altair View Post
    Form the differential equation :-

    'v = f( x - by) + g( x + by), where f and g are twice differentiable'.

    What hint does the statement 'where f and g are twice differentiable' give us?

    And the answer is in the form of Partial Derivatives. How do I know where to use Ordinary derivative and where to use the Partial Derivative?
    v = f( x - by) + g( x + by)

    so:

    v_x = f'( x - by) + g'( x + by)

    v_y = -bf'( x - by) + bg'( x + by)

    Then:

    v_{xx} = f''( x - by) + g''( x + by)

    and

    v_{yy} = b^2f''( x - by) + b^2g''( x + by)

    Hence:

    v_{yy}=b^2v_{xx}

    which is the 1-D wave equation

    RonL
    Last edited by CaptainBlack; February 29th 2008 at 06:00 AM.
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  3. #3
    Member Altair's Avatar
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    In the last equation after hence, shouldn't it be V instead of x? and my question still remains un answered that how will I know that partial differentiation was involved here?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Altair View Post
    In the last equation after hence, shouldn't it be V instead of x? and my question still remains un answered that how will I know that partial differentiation was involved here?
    Yes.

    RonL
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  5. #5
    Member Altair's Avatar
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    Quote Originally Posted by Altair View Post
    my question still remains un answered
    It still does.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Altair View Post
    In the last equation after hence, shouldn't it be V instead of x? and my question still remains un answered that how will I know that partial differentiation was involved here?
    1. because the question is in a section on on partial derivatives.

    2. because you have functions of more than one variable

    RonL
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  7. #7
    Member Altair's Avatar
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    Thanks a lot.
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