Posted by Anonymous on Thursday, March 1, 2012 at 11:37pm.
y^4 - x^4 = 16
4y^3 y' - 4x^3 = 0
y' = x^3/y^3
y'' = (3x^2*y^3 - x^3*3y^2*y')/y^6
= 3x^2(y-xy')/y^4
= 3x^2 (y-x*x^3/y^3)/y^4
= 3x^2 (y^4 - x^4)/y^7
= 48x^2/y^7
or,
y^3 y' = x^3
3y^2 y'^2 + y^3 y'' = 3x^2
3y^2 (x^6/y^6) + y^3 y'' = 3x^2
y^3 y'' = 3x^2 - 3x^6/y^4
y'' = 3x^2 (y^4 - x^4)/y^7
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