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DIFFERENTIAL EQUATIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDIFFERENTIAL EQUATIONS1 Mark
Question
Choose the correct answer from the given four options.General solution of $\frac{\text{dy}}{\text{dx}}+\text{y}\tan\text{x}=\sec\text{x}$ is:
  1. $\text{y}\sec\text{x}=\tan\text{x}+\text{c}$
  2. $\text{y}\tan\text{x}=\sec\text{x}+\text{c}$
  3. $\tan\text{x}=\sec\text{x}+\text{c}$
  4. $\text{x}\sec\text{x}=\tan\text{y}+\text{c}$
✓

Answer

  1. $\text{y}\sec\text{x}=\tan\text{x}+\text{c}$
Solution:
Given differential equation is
$\frac{\text{dy}}{\text{dx}}+\text{y}\tan\text{x}=\sec\text{x}$
This is a linear differential equation
Here, $\text{P}=\tan\text{x},\text{Q}=\sec\text{x},$
$\therefore\text{I.F.}=\text{e}^{\int\tan\text{xdx}}$
$=\text{e}^{\log|\sec\text{x}|}=\sec\text{x}$
Thus, the general solution is
$\text{y}.\sec\text{x}=\int\sec\text{x}.\sec\text{x}+\text{C}$
$\Rightarrow\text{y}.\sec\text{x}=\int\sec^2\text{x}\text{dx}+\text{C}$
$\Rightarrow\text{y}.\sec\text{x}=\tan\text{x}+\text{C}$

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