double derivative y^3-xy=5 PLEASE HELP!!!

Question

i just cant get why i got this wrong and i cant find the answer online, please tell me the answer and how to do this step by step, thank you so much!!

Answer 1

y³ - xy = 5

 

We will use implicit differentiation twice with respect to x:

 

3y²y' - y - xy' = 0     [1]

 

 

6y(y')² + 3y²y" - y' - y' - xy" = 0     [2]

 

 

y" = [2y' - 6y(y')²]/(3y² - x)

 

 

From [1], y' = y/(3y² - x).  Use this expression to substitute into [2].

 

 

y" = [2y/(3y² -x) - 6y³/(3y² - x)²]/(3y² -x)

 

= [2y(3y² - x) - 6y³]/(3y² - x)³ = -2xy/(3y² - x)³