SOLUTION: Given that dy/dx = 3x ^ 2 - 2/(x ^ 2) where x≠0 , and y = 5 when x=1, find the value of y when x=2

From Calculus, the anti-derivative is

    y =  +  + C,  where C = const.


To find C, use the given values y= 5 at x= 1.  It gives

    5 =  +  + C,

    5 = 1 + 2 + C,   so  C = 5 - 1 - 2 = 2.


Thus,  y =  +  + 2.


At x= 2, it gives

      y =  +  + 2 = 8 + 1 + 2 = 11.


ANSWER.  At x= 2,  y= 11.