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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 3 Sub Question 6 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise  Revision Exercise Question 3 Sub Question 6 Maths Textbook Solution.

Answers (1)

Answer:

                Verified

Hint:

Find first derivative and put value in differential equation to verify

Given:

            y=\sqrt{a^{2}-x^{2}}

            x+y\frac{dy}{dx}=0

Solution:

\begin{aligned} &\frac{d y}{d x}=\frac{1}{2} \frac{1}{\sqrt{a^{2}-x^{2}}}(-2 x) \ldots \text { using chain rule } \\ &\frac{d y}{d x}=\frac{-x}{\sqrt{a^{2}-x^{2}}} \end{aligned}

Put in differential equation x+y\frac{dy}{dx}

               \begin{aligned} &=x+\sqrt{a^{2}-x^{2}}\left(\frac{-x}{\sqrt{a^{2}-x^{2}}}\right) \\ &=x-x \\ &=0 \end{aligned}

               = RHS

Hence verified

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