Solve The Differential Equation. Dy Dx = 6x2y2 Jun 2026

Looking at our equation: $$ \frac{dy}{dx} = 6x^2y^2 $$

$$ \int y^{-2} , dy = \int 6x^2 , dx $$

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

The solution is valid for (x \neq \sqrt[3]{C/2}) (to avoid division by zero). Also note that (y=0) is a singular equilibrium solution — you can check it satisfies the original ODE: (y=0 \implies dy/dx = 0) and (6x^2y^2 = 6x^2 \cdot 0 = 0). ✅ solve the differential equation. dy dx = 6x2y2