Integrating factor of the differential equation dy dx +y =1 is: - Vidyadip

MCQ

Integrating factor of the differential equation $\cos\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}\sin\text{x}=1$ is:

A
$\cos\text{x}$
B
$\tan\text{x}$
✓
$\sec\text{x}$
D
$\sin\text{x}$

✓

Answer

Correct option: C.

$\sec\text{x}$

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 we get,
$\text{P}=\tan\text{x}, \text{Q}=\frac{2}{\cos\text{x}}$
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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