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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}}{1+\text{x}^2}$ is:
  • A
    $\text{y}=\frac{1}{2}\log|2+\text{x}^2|+\text{c}$
  • B
    $\text{y}=\frac{1}{2}\log(1+\text{x})+\text{c}$
  • ✓
    $\text{y}=\log\Big(\sqrt{1+\text{x}^2}\Big)+\text{c}$
  • D
    None of these
✓

Answer

Correct option: C.
$\text{y}=\log\Big(\sqrt{1+\text{x}^2}\Big)+\text{c}$

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