Solve The Differential Equation. Dy Dx = 6x2y2 -

[ \int 6x^2 , dx = 6 \cdot \frac{x^3}{3} + C_2 = 2x^3 + C_2 ]

[ \boxed{y(x) = \frac{1}{C - 2x^3}} ]

[ -\frac{1}{y} = 2x^3 + C ]

Set (C = C_2 - C_1):

[ \frac{dy}{dx} = 6x^2 y^2 ]

We are solving:

Right side:

[ \frac{1}{y^2} , dy = 6x^2 , dx ]