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Homework Help: Separation of Variables

  1. Mar 25, 2009 #1
    Good day,

    I have to seperate the variables of the formula (dy/dx) + 1 = - (y/x)
    so I can determine the solution of the differential equation.

    I get:
    (dy/dx) + 1 = - (y/x)
    (dy/dx) = - (y/x) - 1
    (dy) = (- (y/x) - 1)dx

    Though I cannot get rid of the y at the side of dx...
  2. jcsd
  3. Mar 25, 2009 #2
    I don't think you can solve it by separation of variables.
  4. Mar 25, 2009 #3
    Right, thanks. Would it be possible by using Laplace transform?
  5. Mar 26, 2009 #4
    possibly, but it would be much easier to use euler's solution to first order linear differential equations.
  6. Mar 26, 2009 #5
    I already did, but now I want to check the accuracy of the Euler's solution for this differential equation.
  7. Mar 26, 2009 #6


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    Science Advisor

    I recommend the substitution u= y/x. y= xu so y'= xu'+ u and the equation y'= -y/x- 1 becomes xu'+ u= -u- 1 or x du/dx= -2u-1 which is separable.
  8. Mar 26, 2009 #7


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    Homework Helper

    an integrating factor would work as well.
  9. Mar 26, 2009 #8

    Thanks, I get:

    y(x) = (c/x) - (x/2)

    How can I determine the value of the constant now?
  10. Mar 26, 2009 #9


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    Science Advisor

    Are you asking permission?:wink: Certainly if you have some additional condition, you can use that to find c.
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