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

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

Answers (1)

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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