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

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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