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Math Help - Messy Differential Equation!?

  1. #1
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    Messy Differential Equation!?

    I have this differential equation:

    (y-x) dy/dy=2(y^2-dy/dx)

    any help or answers/suggestion please? highly appreciated! thanks in advance!
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  2. #2
    Ted
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    Quote Originally Posted by Yehia View Post
    I have this differential equation:

    (y-x) {\color{red}dy/dy}=2(y^2-dy/dx)

    any help or answers/suggestion please? highly appreciated! thanks in advance!
    The red one is \,\ \frac{dy}{dx} ?
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  3. #3
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    Quote Originally Posted by Ted View Post
    The red one is \,\ \frac{dy}{dx} ?

    YES it is! sorry my bad, it is dy/dx. youre right. can you help?
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  4. #4
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    Isolate the derivative and then put it into differential form:

    (y-x)y'=2y^2-2y'

    y'(y-x+2)=2y^2

    dy(y-x+2)=2y^2 dx

    Now, can you find an integrating factor?
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  5. #5
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    Quote Originally Posted by shawsend View Post
    Isolate the derivative and then put it into differential form:

    (y-x)y'=2y^2-2y'

    y'(y-x+2)=2y^2

    dy(y-x+2)=2y^2 dx

    Now, can you find an integrating factor?

    I follow you till there. But whats an integrating factor? and how can you move the x's to the dx's and the y's to the dy's???? please help further! thank!!
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