help with derivative question

**sterny0** · August 20th 2008, 02:36 PM

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.

the questions are attached

**skeeter** · August 20th 2008, 06:01 PM

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

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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