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Verify that the given functions (explicit or implicit) is a so

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Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: $y = a^{2} - x^{2} x \in (- x, a)$ : $x + y \frac{d y}{d x} = 0 (y \neq = 0)$

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Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

y = a^{2} - x^{2} x \in (- x, a)

x + y \frac{d y}{d x} = 0 (y \neq = 0)

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Text solutionVerified

Solution:

y = a^{2} - x^{2}

Squaring both sides,

\Rightarrow y^{2} = a^{2} - x^{2}

Differentiating both sides w.r.t.

x

\Rightarrow 2 y \frac{d y}{d x} = 0 - 2 x

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

\Rightarrow x + y \frac{d y}{d x} = 0

So, given function is a solution of the corresponding differential equation.

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Question Text	Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: $y = a^{2} - x^{2} x \in (- x, a)$ : $x + y \frac{d y}{d x} = 0 (y \neq = 0)$
Answer Type	Text solution:1
Upvotes	150