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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
Integrating factor of the differntial equation $\cos\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}\sin\text{x}=1$ is :
  • A
    $\sin\text{x}$
  • ✓
    $\sec\text{x}$
  • C
    $\tan\text{x}$
  • D
    $\cos\text{x}$
✓

Answer

Correct option: B.
$\sec\text{x}$
We have,
$\cos\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}\sin\text{x}=1$
Dividing both sides by we get
$\frac{\text{dy}}{\text{dx}}+\frac{\sin\text{x}}{\cos\text{x}}\text{y}=\frac{1}{\cos\text{x}}$
$\Rightarrow \frac{\text{dy}}{\text{dx}}+(\tan\text{x})\text{y}=\frac{1}{\cos\text{x}}$
Comparing with $ \frac{\text{dy}}{\text{dx}}+\text{Py}=\text{Q}$
$\text{P}=\tan\text{x}$
$\text{Q}=\frac{1}{\cos\text{x}}$
Now,
$\text{I.F}=\text{e}^{\int\tan\text{x}}\text{dx}$
$=\text{e}^{\log(\sec\text{x})}$
$=\sec\text{x}$

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