Question

If dy/dx = 2xy^2 , what is d^2y/dx^2 ?

Answer 1

y'' = d^2 y / d x^2
= 2 ( x y' + y. 1 )
= 2x. y' + 2y
= 2x( 2 xy ) + 2y ...........from (1)
= 4 x^2 y + 2y
= 2y ( 2 x^2 + 1 )