Solve the following differential equation: `sqrt(1-x^4)dy=x\ dx`

Explanation

`sqrt{1-x^{4}} d y=x d x`

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Rightarrow d y=frac{x}{sqrt{1-x^{4}}} d x`


By Integrating, we obtain

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int d y=int frac{x}{sqrt{1-x^{4}}} d x`

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Rightarrow y=int frac{x}{sqrt{1-x^{4}}} d x`

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Putting x^{2}=t`

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Rightarrow 2 x d x=d t`

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therefore y=frac{1}{2} int frac{d t}{sqrt{1-t^{2}}}`

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