Solve The Differential Equation. Dy Dx = 6x2y2 «RELIABLE »»

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

Using the power rule for integration $\int y^n , dy = \frac{y^{n+1}}{n+1}$: $$ \int y^{-2} , dy = \frac{y^{-2+1}}{-2+1} = \frac{y^{-1}}{-1} = -\frac{1}{y} $$ solve the differential equation. dy dx = 6x2y2

Let's calculate the integrals separately. Now, we combine the results

∫y-2dy=y-1-1=−1yintegral of y to the negative 2 power space d y equals the fraction with numerator y to the negative 1 power and denominator negative 1 end-fraction equals negative 1 over y end-fraction Use the same rule for x2x squared dy = \frac{y^{n+1}}{n+1}$: $$ \int y^{-2}