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Verify that all members of the family y = (2)1/2 (c - x2)-1/2 are solutions of...

Verify that all members of the family y = (2)1/2 (c - x2)-1/2 are solutions of the differential equation

Find a solution of the initial-value problem. y' = (xy^3)/2 , y(0) = 9

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Answer #1

Given that

The given differential equation is

Substituting the values x = 0 and y = 9 in the given family of functions, we get

Hence, the solution of the initial-value problem y' = (xy^3)/2 , y(0) = 9 is

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