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Explain Solution R.D.Sharma Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 26 Maths Textbook Solution.

Answers (1)

Answer: \sin x\sin y=c

Hint: You must know about trigonometric identities.  

Given:\tan y\; dx+\tan \: x\; dy=0

Solution:\tan y\; dx+\tan \: x\; dy=0

          \begin{aligned} &\Rightarrow \tan x d y=-\tan y d x \\ &\Rightarrow \frac{1}{-\tan y} d y=\frac{1}{\tan x} d x \\ &\Rightarrow \cot y d y=-\cot x d x\left(\because \frac{1}{\tan x}=\cot x\right) \end{aligned}

           Integrating both sides

          \begin{aligned} &\Rightarrow \int \cot y d y=-\int \cot x d x \\ &\Rightarrow \log |\sin y|=-\log |\sin x|+\log c \\ &\Rightarrow \log |\sin y|+\log |\sin x|=\log c \\ &\Rightarrow \log |\sin y \sin x|=\log c(\because \log a+\log b=\log a b) \\ &\Rightarrow \sin y \sin x=c \end{aligned}

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