The solution of the equation ( 1 + x 2 ) d y d x = 1 is:

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Solution

Q.
The solution of the equation $(1 + x^{2}) \frac{d y}{d x} = 1$ is:

1 $y = \log (1 + x^{2}) + C$

2 $y + \log (1 + x^{2}) + C = 0$

3 $y - \log (1 + x) + C$

4 $y = \tan^{- 1} x + C$

Ans.
(4)

Ans. $y = \tan^{- 1} x + C$

Explanation:

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

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

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

On integrating, $y = \tan^{- 1} x + C$

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