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Math Help - A really simple integration...

  1. #1
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    A really simple integration...

    Find the particular solution for dy/dx=(y-5)/x, using the point y(0)=7

    I got y-5=Ax (or ln(y-5)=ln(x)+c)

    For both of which there is no way to find A or c...I had this question in a test, and wrote it was impossible to find the particular solution with the given point (I believe the examiner made an error..) am I correct?
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  2. #2
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    Quote Originally Posted by Helpsmeplease View Post
    For both of which there is no way to find A or c...I had this question in a test, and wrote it was impossible to find the particular solution with the given point (I believe the examiner made an error..) am I correct?
    You are wrong, you need to use y(0)=7 to find A or c.

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  3. #3
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    Yea...and when you sub x=0 into ln(x) you get an error...and 7-5 doesnt = 0*A...so....
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  4. #4
    MHF Contributor chisigma's Avatar
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    The DE can be written as...

    x y' - y = - 5 (1)

    ... so that it is a linear first order DE. Neccessary condition to have a solution is that the coefficient of the term y' doesn't vanish... but the 'initial condition' is for x=0 so that that isn't verified...

    Kind regards

    \chi \sigma
    Last edited by chisigma; June 18th 2010 at 11:50 PM. Reason: LaTex has been used...
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  5. #5
    MHF Contributor chisigma's Avatar
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    ... but if we swap the x and y variables the DE becomes...

    x'= \frac{x}{y-5} , x(7)=0 (1)

    ... the solution of which is x=0... very easy ...

    Kind regards

    \chi \sigma
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