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Finding general solution for ODE.

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data

    For the following differential equation:
    1) Provide the general solution
    2) Discuss for which values of x the solution is defined.
    3) Find the solution of the initial value problem y(0) = 3


    2. Relevant equations
    dy/dx = (y+3)(y-5)


    3. The attempt at a solution
    1) so I seperate variables and get (1/8)*(log(y-5)-log(y+3)) = x + C after integration.
    Now i need to solve for x right? How would I go about doing this? Can't seem to figure out how to rearange.
    2) I dont think i can do this until i find the general solution? But once its found do i just find its domain?
    3) For this i just substitute the initial values in, solve for C and then place back in equation?
     
    Last edited: Mar 11, 2012
  2. jcsd
  3. Mar 11, 2012 #2

    Ray Vickson

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    How did you get ∫dy/[(y+3)(y-5)] = (1/8)[log(x-5)-log(x-3)]?

    RGV
     
  4. Mar 11, 2012 #3
    sorry replace the x's with y's that was a typo. And i did it by splitting into partial fractions then integrating each term simply. Was that not correct?
     
  5. Mar 12, 2012 #4

    Ray Vickson

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    You don't need to solve for x; it is already done---just read your own equation! Now, if you wanted to solve for y as a function of x, that would involve a bit more effort, but is still just elementary algebra: use standard properties of log to do it.

    RGV
     
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