Solve - dydx-1-x21-y2

dydx=(1+x^2)(1+y^2) dy1+y^2=(1+x^2)dx ∫dy1+y^2=∫ (1+x^2)dx tan^ 1y = ∫ dx + ∫ x^2 dx tan^ 1y=x+x^33+C ...

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Variable Separable Method

Solve : dydx...

Question

Solve :
$\frac{d y}{d x} = (1 + x^{2}) (1 + y^{2})$

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Solution

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

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

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

\frac{d y}{d x} = 1 + y^{2}

\frac{d y}{d x} + \sqrt{\frac{1 - y^{2}}{(1 + y)^{2}}} = 0

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