The solution of the equation (1 + x^2 ) dy dx = 1 is - Vidyadip

MCQ

The solution of the equation $(1 + {x^2})\frac{{dy}}{{dx}} = 1$ is

A
$y = \log (1 + {x^2}) + c$
B
$y + \log (1 + {x^2}) + c = 0$
C
$y - \log (1 + x) = c$
✓
$y = {\tan ^{ - 1}}x + c$

✓

Answer

Correct option: D.

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

d
(d) $(1 + {x^2})\frac{{dy}}{{dx}} = 1$ ==>$\frac{{dy}}{{dx}} = \frac{1}{{1 + {x^2}}}$

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

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