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First order nonlinear ordinary differential equation

  1. Jul 6, 2010 #1
    1. The problem statement, all variables and given/known data

    y' + Ay2 = B

    A & B are constants and y is a function of x

    Find the general solution to the differential equation. (Find y(x)).

    2. Relevant equations



    3. The attempt at a solution

    This differential equation came up when I was trying to solve a problem in physics. I have just learned to solve basic linear differential equations from high school and don't know how to start solving this or even if it's solvable without a computer. If somebody could give me a push in the right direction or tell me what I could study to be able to solve it, it would have been very nice :)

    The only thing I've tried is differentiating it with respect to x, and getting this:

    y'' + 2Ayy' = 0

    I don't find this any easier because I have the y×y' there. So, any help would be nice ;)
     
  2. jcsd
  3. Jul 6, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    Write the ODe in the following way:
    [tex]
    \frac{dy}{dx}=B-Ay^{2}
    [/tex]
    This equation is separable, divide by [tex]B-Ay^{2}[/tex] and integrate

    Mat
     
  4. Jul 6, 2010 #3
    This one is "separable" - which means it's solvable using integration. Rearrange to get
    [tex]
    \frac{dy}{B-Ay^2} = dx,
    [/tex]
    and do two integrals. There will be significant algebraic rearrangement involved to solve for y in terms of x.

    You should probably reference a differential equations book.
     
  5. Jul 6, 2010 #4
    Thanks for the answers!
    That was really less painful than I expected :tongue: Don't know why I didn't think of that :uhh:
    Next problem now is solving the integral, but I think I should be able to do that myself
     
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