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Verify that y^(2) = 4(1-x^(2)) is a solu...

Verify that `y^(2) = 4(1-x^(2))` is a solution of the differential equation `xy y' + x(y')^(2) - y y' = 0`

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`y^(2) = 4(1-x^(2))`
Differentiating both sides w.r.t. twice, we get
`2y y' = -8x`
`rArr y y' = -4x` ...(1)
`y y' + y^(2) = -4` ...(2)
Multiplying it by x we get
`x y y' + x y^(2) = -4x`
= y y' from (1)
`rArr x y y' xy^(2) - y y' = 0` which is same as the given differential equation, therefore the given function is a solution of the given differential equation.
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