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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
Question
Choose the correct answer from the given four option.
Integrating factor of the differential equation $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\tan\text{x}-\sec\text{x}=0$ is:
  1. $\cos\text{x}$
  2. $\sec\text{x}$
  3. $\text{e}^{\cos\text{x}}$
  4. $\text{e}^{\sec\text{x}}$
✓

Answer

  1. $\sec\text{x}$

Solution:

Given that, $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\tan\text{x}-\sec\text{x}=0$

$\Rightarrow\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\tan\text{x}=\sec\text{x}$

$\Big($It is a linear differential equation of form $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{P}\text{y}=\text{Q}\Big)$

Here, $\text{P}=\tan\text{x},\text{Q}=\sec\text{x}$

$=\text{I.F.}=\text{e}^{\int\text{Pdx}}$

$=\text{e}^{\int\tan\text{x}\text{dx}}$

$=\text{e}^{(\log\sec\text{x})}$

$=\sec\text{x}$

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