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Homework Help: Stuck on separable equation (algebra prob?)

  1. Apr 12, 2010 #1
    stuck on separable equation (algebra prob??)

    1. The problem statement, all variables and given/known data
    y' = 2x/(1+2y) y(2) = 0

    (1+2y)dy = 2xdx

    integrate both sides

    y + y^2 = x^2 + c

    I am stuck trying to put in in explicit form, so y = ....

    is this completing the square or something?
    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 12, 2010 #2

    Dick

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    Re: stuck on separable equation (algebra prob??)

    First find c. Then, sure, if you want to solve for y(x) then complete the square.
     
  4. Apr 12, 2010 #3
    Re: stuck on separable equation (algebra prob??)

    c = y + y^2 - x^2

    c = 0 + 0^2 - (2^2)

    c = 4

    y + y^2 = x^2 + 4

    But i still dont see how complteting square will pu equation into form y = ... ???
     
  5. Apr 12, 2010 #4

    Dick

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    Re: stuck on separable equation (algebra prob??)

    c=4 doesn't work. 0 isn't equal to 2^2+4. Can you fix that? Why don't you complete the square in y before you decide it doesn't work?
     
  6. Apr 12, 2010 #5
    Re: stuck on separable equation (algebra prob??)

    should be -4

    c = y + y^2 - x^2

    c = 0 + 0^2 - (2^2)

    c = -4

    y + y^2 = x^2 - 4

    COmpleting square is confusing me. How does that help with a DE? It is used to find the roots, but im trying to get the equation to look like: y = something
    thank you
     
  7. Apr 12, 2010 #6

    Dick

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    Re: stuck on separable equation (algebra prob??)

    You are trying to find the roots. You are trying to solve for y. Can you write y+y^2 in the form (y+A)^2-B by finding the constants A and B? Wouldn't that help to solve for y?
     
  8. May 26, 2010 #7
    Re: stuck on separable equation (algebra prob??)

    How do i get the equation y + y^2 = x^2 - 4 into the form y= ....

    the answer key uses the quadratic formula but I am confused what a, b and c would be in the equation. ( -b +/- root b^2 - 4ac / 2a)

    i can rearrange so that its: y^2 + y - x^2 + 4 = 0,

    and i can see that a must be "1" .. but what is b and c when equation is in this form??
     
  9. May 26, 2010 #8

    Dick

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    Re: stuck on separable equation (algebra prob??)

    b=1 (since it's the coefficient of the y) and c=(-x^2+4) (since it's the 'constant' part independent of y).
     
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