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$\frac{d y}{d x}=\sqrt{4-y^{2}}(-2


The given differential equation is:

$\frac{d y}{d x}=\sqrt{4-y^{2}}$

Separating the variables, we get:

$\Rightarrow \frac{d y}{\sqrt{4-y^{2}}}=d x$

Now, integrating both sides of this equation, we get:

$\int \frac{d y}{\sqrt{4-y^{2}}}=\int d x$

$\Rightarrow \sin ^{-1} \frac{y}{2}=x+\mathrm{C}$

$\Rightarrow \frac{y}{2}=\sin (x+\mathrm{C})$

$\Rightarrow y=2 \sin (x+\mathrm{C})$

This is the required general solution of the given differential equation.

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