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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: $y = 1 + x^{2} :$ $y^{'} = \frac{x y}{1 + x ^{2}}$ $y = A x$ : $x y^{'} = y (x \neq = 0)$

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

y = 1 + x^{2} :

y^{'} = \frac{x y}{1 + x ^{2}}

y = A x

x y^{'} = y (x \neq = 0)

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Text solutionVerified

Solution:

y = 1 + x^{2}

differnetiate with respect to x

y^{'} = \frac{x}{1 + x ^{2}}

multiplying and dividing of right side with

1 + x^{2}

y^{'} = \frac{x 1 + x ^{2}}{1 + x ^{2}}

y^{'} = \frac{x y}{1 + x ^{2}}

hence proved

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