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Verify that all members of the family y=(c-x^2)^(-1/2) are solutions of the differential equation y'=xy^3. Can anyone help me with this please?

1 Answer

Vinícius Ferraz

Jun 18, 2018

See below.

Explanation:

#y = (c - x^2)^(-1/2)#

#y' = -1/2 * (c - x^2)^(-3/2) * (-2x)#

#y^3 = (c - x^2)^(-3/2)#

#(y')/(y^3) = +x#

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