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Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.3 question 21 sub question (ii)

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Answer:

Function satisfies the given differential equation

Hint:

Modify the function by taking squares on both sides.

Given:

y=\pm \sqrt{a^{2}-x^{2}}

Solution:

Given, y=\pm \sqrt{a^{2}-x^{2}} as a function

Taking squares on both sides

\begin{aligned} &\Rightarrow y^{2}=\left(\sqrt{a^{2}-x^{2}}\right)^{2} \\\\ &\Rightarrow y^{2}=a^{2}-x^{2} \end{aligned}

Now differentiating with respect to x

\Rightarrow 2 y \frac{d y}{d x}=-2 x

\begin{aligned} &\Rightarrow \frac{d y}{d x}=-\frac{x}{y} \\\\ &\Rightarrow y \frac{d y}{d x}=-x \\\\ &\Rightarrow x+y \frac{d y}{d x}=0 \end{aligned}

Thus, the function satisfies the differential equation.

 

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