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Thread: Differential equation of the family of curves y=c(x-c)^2

  1. #1
    Member Vinod's Avatar
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    Post Differential equation of the family of curves y=c(x-c)^2


    Find the differential equation of the family of curves y=c(x-c)^2 where c is a parameter.

    I don't know the solution to this problem. Shall i get help to get the solution to this problem?
    Okay,
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  2. #2
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    Re: Differential equation of the family of curves y=c(x-c)^2

    Take the \ln of both sides

    \ln y = \ln c + 2\ln (x-c)

    Then differentiate

    \frac{y'}{y} = \frac{2}{x-c}

    solve for c and sub back into original ODE.

    You know, there are many ODEs that has this as a solution.
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  3. #3
    Member Vinod's Avatar
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    Re: Differential equation of the family of curves y=c(x-c)^2

    Quote Originally Posted by Danny View Post
    Take the \ln of both sides

    \ln y = \ln c + 2\ln (x-c)

    Then differentiate

    \frac{y'}{y} = \frac{2}{x-c}

    solve for c and sub back into original ODE.

    You know, there are many ODEs that has this as a solution.
    Danny,
    MHF helper,
    Hello,
    I got the answer to the problem. Thanks.
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