Solve The Differential Equation. Dy Dx = 6x2y2 ★

The general solution to the differential equation $\frac{dy}{dx} = 6x^2y^2$ is given by $y = \frac{1}{-2x^3 - C}$.

If (y(0) = 1): (1 = \frac{1}{C - 0} \implies C = 1) So (y(x) = \frac{1}{1 - 2x^3}). solve the differential equation. dy dx = 6x2y2

Using the power rule for $x$: $$ \int 6x^2 , dx = 6 \left( \frac{x^3}{3} \right) = 2x^3 $$ usually denoted as $C$.

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

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

Now, we combine the results. We only need one constant of integration, usually denoted as $C$.