Solve The Differential — Equation. Dy Dx = 6x2y2

[ \int y^{-2} , dy = -y^{-1} + C_1 = -\frac{1}{y} + C_1 ]

Let's calculate the integrals separately. solve the differential equation. dy dx = 6x2y2

After integration, we have: $-\frac{1}{y} = 2x^3 + C$. To solve for $y$, we rearrange the equation: $\frac{1}{y} = -2x^3 - C$. Thus, $y = \frac{1}{-2x^3 - C}$. [ \int y^{-2} , dy = -y^{-1} +

y-2dy=6x2dxy to the negative 2 power d y equals 6 x squared d x 2. Integrate both sides Apply the power rule for integration, , to both sides of the equation: [ \int y^{-2}