What is integrating factor of dy dx +y = ? - Vidyadip

MCQ

What is integrating factor of $\frac{\text{dy}}{\text{dx}}+\text{y}\sec\text{x}=\tan\text{x}?$

✓
$\sec\text{x}+\tan\text{x}$
B
$\log(\sec\text{x}+\tan\text{x})$
C
$\text{e}^{\sec\text{x}}$
D
$\sec{\text{x}}$

✓

Answer

Correct option: A.

$\sec\text{x}+\tan\text{x}$

We have,
$\frac{\text{dy}}{\text{dx}}+\text{y}\sec\text{x}=\tan\text{x}$
Comparing with We get,
$\text{P}=\sec{\text{x}}, \text{Q}=\tan{\text{x}}$
Now,
$\text{I.F}=\text{e}^{\int\sec\text{x}\text{dx}}$
$=\text{e}^{\log(\sec\text{x}+\tan\text{x})}$
$=\sec\text{x}+\tan\text{x}$

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