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Math Help - Simplifying an equation containing both a first order and second order differential

  1. #1
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    Simplifying an equation containing both a first order and second order differential

    Hi,

    Apologies in advance if this is a simple/stupid question - I am a biologist...

    I have an equation of the form:

    z . d^2y/dx^2 = t . dy/dx + r

    where z, t and r are all constants. I am wondering if there is a simpler way to state this? With the eventual aim of having the equation in the form t = ..... as at the moment I cannot see how t relates to dy/dx as the d^2y/dx^2 is variable.

    Many thanks in advance.
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  2. #2
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    Re: Simplifying an equation containing both a first order and second order differenti

    You have zy''= ty'+r

    so zy''-r= ty'

    \frac{zy''-r}{y'}= t

    but that would be too simple and is a fucntion of differentials.

    Is it fair to guess you need to solve the DE first, then solve for t? Remember t is constant, do you want to make this the subject?
    Last edited by pickslides; September 21st 2011 at 03:43 PM. Reason: fix latex
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  3. #3
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    Re: Simplifying an equation containing both a first order and second order differenti

    Ah sorry, t is dependent on dy/dx so it is not constant. I am hoping to be able to make the general statement that assuming z and r are constant, t is proportional to some function of dx/dy. I dont know if this is possible?

    Thanks for the quick reply!
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