Solve The Differential Equation. Dy Dx = 6x2y2 Patched

Using the power rule for integration $\int y^n , dy = \frac{y^{n+1}}{n+1}$: $$ \int y^{-2} , dy = \frac{y^{-2+1}}{-2+1} = \frac{y^{-1}}{-1} = -\frac{1}{y} $$

y=1−(2x3+C)y equals the fraction with numerator 1 and denominator negative open paren 2 x cubed plus cap C close paren end-fraction solve the differential equation. dy dx = 6x2y2

Alternatively, we can simply leave the negative sign in front: $$ y = -\frac{1}{2x^3 + C} $$ Using the power rule for integration $\int y^n