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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 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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