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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 $\cos\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\sin\text{x}=1$ is:
  1. $\cos\text{x}$
  2. $\tan\text{x}$
  3. $\sec\text{x}$
  4. $\sin\text{x}$
✓

Answer

  1. $\sec\text{x}$

Solution:

we have, $\cos\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\sin\text{x}=1$

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

This is a linear differential equation.

On comparing it with $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{P}\text{y}=\text{Q},$ we get

$\text{P}=\tan\text{x}$ and $\text{Q}=\sec\text{x}$

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

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

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