Solve The Differential Equation. Dy Dx 6x2y2 [verified] Official

Note on Constants: Since $C$ is an arbitrary constant, $-C$ is also an arbitrary constant. For simplicity, we can just rename $-C$ to $C$ (or $C_1$). $$ \frac{1}{y} = -2x^3 + C $$

y-2dy=6x2dxy to the negative 2 power d y equals 6 x squared d x 2. Integrate Both Sides Now, apply the integral sign to both sides of the equation: solve the differential equation. dy dx 6x2y2

[ \frac{dy}{dx} = 6x^2 y^2 ] looks innocent. It yields to separation of variables in two lines. But its solutions contain an explosive secret—a singularity at a finite (x)—revealing the boundary between neat algebra and the wilder behavior of nonlinear systems. Note on Constants: Since $C$ is an arbitrary

Now we put the results of both integrals back together. Usually, we combine the constants of integration from both sides into a single constant $C$ on the right side. Integrate Both Sides Now, apply the integral sign