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

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

$$ y(x) = -\frac{1}{2x^3 + C} $$

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

Now, integrate both sides of the equation: $\int \frac{dy}{y^2} = \int 6x^2 dx$. The left side integrates to $-\frac{1}{y}$ and the right side to $2x^3 + C$, where $C$ is the constant of integration. solve the differential equation. dy dx = 6x2y2

When we divided by $y^2$ in Step 1, we made the assumption that $y \neq 0$. If $y=0$, that division would have been invalid. Therefore, we must check if $y=0$ is a solution to the original differential equation. Now, we combine the results

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, $y = \frac{1}{-2x^3 - C}$. The left side integrates to $-\frac{1}{y}$ and the