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Math Help - Simplifying non-linear ODE

  1. #1
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    Simplifying non-linear ODE

    Hi all,

    So I have the equation:

    dx/dt = (x2+xt)/t2 where x(1) = 2

    I am aware that I can make a substitution by letting y equation a function of x and t, however I am unsure as to what I should let y equal and how I would plug it in and end up solving the equation.

    Any help is much appreciated!

    Thanks
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  2. #2
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    Re: Simplifying non-linear ODE

    \frac{dx}{dt}=\left(\frac{x}{t}\right)^2+\left( \frac{x}{t}\right)

    Does that suggest anything?
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  3. #3
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    Re: Simplifying non-linear ODE

    Ya I got that! So then I get F(y) = ysq + y

    Not sure how to solve this though :S
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  4. #4
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    Re: Simplifying non-linear ODE

    Use y=x/t (so that x=ty) and differentiate with respect to t.

    dx/dt = .........
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  5. #5
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    Re: Simplifying non-linear ODE

    okay I think I got it, this is just taking a while to click, I just need to remember you can treat most of it like normal algebra.

    Did you get the constant = -0.5?

    - Upon substitution I get: 1/y^2 dy = 1/t dt

    chugging through and putting in initial conditions I get:

    - Ln(t) - 1/y = A

    Thanks again, really appreciated.
    Last edited by acid_rainbow; February 14th 2013 at 09:44 AM.
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  6. #6
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    Re: Simplifying non-linear ODE

    I think you have it.

    In case I mislay my bit of paper again, the solution I got was x=\frac{2t}{1-2\ln 2}.

    and you're welcome by the way. I'm relearning differential equations myself at the moment.
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