Use explicit differentiation to solve y^4 - y^2 = -x^2

Question

Explicit differentiation to solve y^4 - y^2 = -x^2

Answer 1

Student,

 

I am pretty sure you meant to say IMPLICIT differentiation.

 

y⁴ - y² = -x²

 

4y³y' - 2yy' = -2x

 

2y³y' - yy' = -x

 

yy'(2y² - 1) = -x

 

y'(x,y) = -x / [y(2y² - 1)] = x / [y(1 - 2y²)]