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Math Help - existance of a specific diff. eq.

  1. #1
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    existance of a specific diff. eq.

    hi,

    i have the following question:

    is there an ordinary 2nd order, linear differential equation,

    which solution is the family of circles:

    (x-c1)^2+y^2 = c2^2?

    and if there is, find such an example.

    i am clueless...
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  2. #2
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    anyone?
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  3. #3
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    Quote Originally Posted by vonflex1 View Post
    hi,

    i have the following question:

    is there an ordinary 2nd order, linear differential equation,

    which solution is the family of circles:

    (x-c1)^2+y^2 = c2^2?

    and if there is, find such an example.

    i am clueless...
    Differentiate the given equation with respect to x. 2(x- c_1)+ 2y y'= 0. Write that as 2y y'= 2x- 3c_1 and differentiate again: 2y y"+ 2 y'^2= 2.
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