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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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