Find the order and the degree of the differential equation $\sqrt{1 - y^{2}} d x = \sqrt{1 - x^{2}} d y$ .

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Solution

Given the differential equation,
$\sqrt{1 - y^{2}} d x = \sqrt{1 - x^{2}} d y$ can be written as
$\frac{d y}{d x} = \frac{\sqrt{1 - y^{2}}}{\sqrt{1 - x^{2}}}$ .
Which is clearly a first order and first degree differential equation.

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