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  • Explain solution RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 20 maths

Explain solution RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 20 maths

Answers (1)

Answer:

 xy=Ce^{-y}

Hint:

 First separate the variables and then use simple Integrating to solve the question.

Given:

 y\, dx+(x+xy)dy=0

Solution:

\begin{aligned} &\Rightarrow y\, dx=-x(1+y)dy \\ &\Rightarrow \frac{dx}{x}=-\left ( \frac{1+y}{y} \right )dy \\ &\Rightarrow \int \frac{1}{x}=-\int \left ( \frac{1}{y}+1 \right )dy \\ &\Rightarrow log\, x=-log\, y-y+log\, C \\ &\Rightarrow log\, x+log\, y-log\, C=-y \\ &\Rightarrow log\frac{xy}{c}=-y \\ &\Rightarrow \frac{xy}{c}=e^{-y} \\ &\Rightarrow xy=Ce^{-y} \end{aligned}

Hence, the answer is

xy=Ce^{-y}

Posted by

Gurleen Kaur

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