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Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Revision Exercise (RE) Question 65 Subquestion (iii) textbook solution.

Answers (1)

Answer          : y=\sec x

Hint                : You must know the rules of solving differential equation and integration

Given             : \frac{d y}{d x}=y \text { tan } x \quad, y=1 \text { where }, x=0

Solution        :  \frac{d y}{d x}=y \text { tan } x

                         \frac{1}{y} d y=\tan x d x

Integrating both sides,

 \begin{aligned} &\int \frac{1}{y} d y=\int \tan x d x \\ &\Rightarrow \log y=\log |\sec x|+C \end{aligned}

Now, x=0,y=1


\begin{gathered} \log 1=\log 1+C \\ C=0 \end{gathered}

Put value of c ,

\begin{aligned} \log y &=\log |\sec x|+0 \\ \log y &=\log |\sec x| \\ y &=\sec x \end{aligned}

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