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Math Help - Homogeneous Diff Eqn's

  1. #1
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    Homogeneous Diff Eqn's

    Can anyone help me with this question, please?

    Find a diŽerential equation whose solution is the family of parabolas
    with vertices and foci on the
    x-axis.
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  2. #2
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    Everything starts from the equation of the parabola. Parabolas with vertices and foci on the abscissa all have the following equation: y^2=2px where p is the distance between the focus and the origin of the coordinate system (in this case its the distance along the abscissa). Applying derivative with respect to x and you get the following differential equation: 2yy'=2p where you can substitute 2p with general constant term C providing the constraint C>0 since it carries the information about the distance which cannot be negative.

    Hope this helps.
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  3. #3
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    Thanks, MathoMan! It does help. I found the answer in the book, which states that the differential equation is 2XY'=Y. Gonna try and figure out how that relates to your equation. Thanks again!
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