The general solution of the D.E. dxdy=(1−x2)(1−y2) is

∫1−y2dy=∫1−x2dx⇒sin−1y=2x1−x2+21sin−1x+C⇒2sin−1y−sin−1x=x1−x2+C.

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The general solution of the D.E. {dy}{dx}=({1-x^{2}})({1-y^{2}

Question

The general solution of the D.E. $\frac{d y}{d x} = (1 - x^{2}) (1 - y^{2})$ is

sin^{- 1} y - sin^{- 1} x = x 1 - x^{2} + C

2 sin^{- 1} y - sin^{- 1} x = x 1 - x^{2} + C

2 sin^{- 1} y - sin^{- 1} x = C

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Alexander Discussed

The general solution of the D.E.

\frac{d y}{d x} = (1 - x^{2}) (1 - y^{2})

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\int \frac{d y}{1 - y ^{2}} = \int 1 - x^{2} d x

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

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

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Question Text	The general solution of the D.E. $\frac{d y}{d x} = (1 - x^{2}) (1 - y^{2})$ is
Answer Type	Text solution:1
Upvotes	150