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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
Question
What is integrating factor of $\frac{\text{dy}}{\text{dx}}+\text{y}\sec\text{x}=\tan\text{x}?$
  1. $\sec\text{x}+\tan\text{x}$
  2. $\log(\sec\text{x}+\tan\text{x})$
  3. $\text{e}^{\sec\text{x}}$
  4. $\sec{\text{x}}$ 
✓

Answer

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

Solution:

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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