1y2dy=6x2dxthe fraction with numerator 1 and denominator y squared end-fraction d y equals 6 x squared d x This can also be written using a negative exponent as:
[ \int y^{-2} , dy = \int 6x^2 , dx ]
[ \frac{1}{y^2} , dy = 6x^2 , dx ]
Left side:
(Note: Depending on how the constant is defined, this may also appear as $y = \frac{1}{C - 2x^3}$. Both forms are mathematically equivalent.) solve the differential equation. dy dx = 6x2y2