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  • Provide solution for RD Sharma maths class 12 chapter 21 Differential Equation exercise Fill in the blank question 34

Provide solution for RD Sharma maths class 12 chapter 21 Differential Equation exercise Fill in the blank question 34

Answers (1)

Answer:

 Hyperbola

Given:

The differential equation xdy + ydx = 0 represents the family of ____

Hint:

 By the help of integral sums will get solve.

Solution:

\begin{aligned} &xdy + ydx=0 \\ &\Rightarrow xdy = -ydx \\ &\Rightarrow \frac{dy}{y}=-\frac{dx}{x} \end{aligned}

Integrating both sides

\begin{aligned} &\int \frac{dy}{y}=-\int \frac{dx}{x} \\ &\Rightarrow log\, y=-log\, x+log \, C \\ &\Rightarrow log\, y+log\, x=log \, C \\ &\therefore xy=C \end{aligned}

So, the above differential equation represents the Hyperbola.

Posted by

Gurleen Kaur

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