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Math Help - Differential Equation

  1. #1
    Member Altair's Avatar
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    Differential Equation

    Find the differential equation for a parabola with latus rectum 4a and whose axis are parallel to x-axis.
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Altair View Post
    Find the differential equation for a parabola with latus rectum 4a and whose axis are parallel to x-axis.
    The equation of the parabola satisfying the given requirements is (y-k)^2 = 4ax. So the solution of the DE is

    (y - k)^2 = 4ax .... (1)

    => y^2 - 2ky + k^2 = 4ax .... (2)

    Differentiate (2) with respect to x:

    2y \, y' - 2k\, y' = 4a .... (3)

    Obviously k needs to be eliminated from (3). k can be got from (1) in terms of x, y and a. Substitute this result into (3).
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