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Math Help - help with derivative question

  1. #1
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    Exclamation help with derivative question

    could some1 show me how to do this question. i don't know wat im suppose to do.

    By separating the variables, find the "general solutions" of the following differential equations. Then for each case find the particular solution of each that satisfy the given conditions.

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  2. #2
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    x\sqrt{1-y^2} \, dx = -y\sqrt{1-x^2} \, dy

    separate variables ...

    \frac{x}{\sqrt{1-x^2}} dx = \frac{-y}{\sqrt{1-y^2}} dy

    integrate both sides using substitution, then use your initial condition to find the constant of integration.


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

     \frac{dy}{dx} = \frac{x(2y^2 + 1)}{y(x^2 - 1)}

    \frac{y}{2y^2+1} dy = \frac{x}{x^2-1} dx<br />

    this is a straight-forward integration involving logs ... go for it.
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