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Please solve RD Sharma class 12 chapter Differential Equations exercise 21.7 question 45 sub question (i) maths textbook solution

Answers (1)


Answer: z=\sec x

Hint: Separate the terms of x and y and then integrate them.

Given: \frac{d y}{d x}=y \tan x, y(0)=1

Solution: \frac{d y}{d x}=y \tan x, y(0)=1

        \Rightarrow \frac{d y}{y}=\tan x \; d x

        Integrating both sides

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

        Now Given that y=1 \text { when } x=0

        \begin{aligned} &1=c \sec (0) \Rightarrow c=1 \quad[\sec 0=1] \\\\ &y=(1) \sec x \Rightarrow y=\sec x \end{aligned}

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