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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 differential equation $(1 + {x^2})\frac{{dy}}{{dx}} = x(1 + {y^2})$ is
  • ✓
    $2{\tan ^{ - 1}}y = \log (1 + {x^2}) + c$
  • B
    ${\tan ^{ - 1}}y = \log (1 + {x^2}) + c$
  • C
    $2{\tan ^{ - 1}}y + \log (1 + {x^2}) + c = 0$
  • D
    None of these
✓

Answer

Correct option: A.
$2{\tan ^{ - 1}}y = \log (1 + {x^2}) + c$
a
(a) $(1 + {x^2})\frac{{dy}}{{dx}} = x(1 + {y^2})$ ==>$\frac{1}{{1 + {y^2}}}dy = \frac{x}{{1 + {x^2}}}dx$

On integrating, we get ${\tan ^{ - 1}}y = \frac{1}{2}\log (1 + {x^2}) + c$

==> $2{\tan ^{ - 1}}y = \log (1 + {x^2}) + c$.

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