Find the general solution of the differential equations `frac{dy}{dx}=sqrt{(4-y^2)}` (-2

Explanation

It is given that

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

`int(\frac{1}{\sqrt{4-y^{2}}}) \dy=dx \text { (arranging) }`

on integration, we get

`\int(\frac{1}{\sqrt{4-y^{2}}}) d y=\int 1 \cdot d x+C`

`\int \frac{1}{\sqrt{a^{2}-x^{2}}}=\sin ^{-1} \frac{x}{a}+C`

` \sin ^{-1}(\frac{y}{2})=x+c`

` \frac{y}{2}=\sin (x+c)`

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