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Math Help - Differential Equation<don't know what method to use

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    Differential Equation<don't know what method to use

    Code:
    (x^2+y^2-5)dx=(x+xy)dy
    What method should I use to find the General Solution of this?
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    Re: Differential Equation<don't know what method to use

    Quote Originally Posted by shinmei View Post
    Code:
    (x^2+y^2-5)dx=(x+xy)dy
    What method should I use to find the General Solution of this?
    Well my (admittedly limited) differential equation library comes up with nothing. Neither does Wolfram|Alpha. That's hardly the last word but I'd say you're going to need an approximation technique.

    -Dan
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    Re: Differential Equation<don't know what method to use

    (x^2+y^2-5)dx=(x+xy)dy

    \frac{dy}{dx}(x+xy)=x^2+y^2-5

    \frac{dy}{dx}=\frac{x^2+y^2-5}{x+xy}

    \int \frac{dy}{dx} dx=\int \frac{x^2+y^2-5}{x+xy} dx

    \int dy=\int \frac{x^2+y^2-5}{x+xy} dx

    dy is the same as 1.dy, and so integrating 1 (which is congruent to y^0) with respect to y will give you \frac{y^1}{1} = y

    y=\int \frac{x^2+y^2-5}{x+xy} dx

    Unfortunately, my high school understanding of calculus doesn't give me a method to integrate the RHS of this equation. If someone here could do that then you should have your general solution. I have no idea if this is correct though, just a long shot.
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    Re: Differential Equation<don't know what method to use

    ^ the problem to me seems to be separating the unknowns x and y onto the different sides of the equation. I can't seem to factorise them myself.
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