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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
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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