Question

if x^2+y^2=2y.. show that d^2y/dx^2=1/(1-y)^3

Answer 1

something seems wrong with this

Answer 2

As given :- x^2 + y^2 = 2y
Therefore y = (x^2 + y^2) / 2

Hence d^2 (y) / dx^2 = dy/dx * dy/dx = (dy/dx)^2

dy/dx = d [(x^2 + y^2) / 2] / dx
= d(x^2/2) + d(y^2 /2) / dx
= (1/2) (2x) + (1/2) (2y)
= x + y

Therefore ( dy/dx )^2 = x^2 + y^2 + 2xy

Here on replacing the value of x from the given eqaution we get the answer

Answer 3

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