Solved example of separable differential equations
Group the terms of the differential equation. Move the terms of the $y$ variable to the left side, and the terms of the $x$ variable to the right side
Integrate both sides, the left side with respect to $y$, and the right side with respect to $x$
The integral of a constant by a function is equal to the constant multiplied by the integral of the function
Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function
Simplify the fraction
Solve the integral $\int3y^2dy$ and replace the result in the differential equation
The integral of a constant by a function is equal to the constant multiplied by the integral of the function
Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function
Solve the integral $\int2xdx$ and replace the result in the differential equation
As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration
Removing the variable's exponent
Cancel exponents $3$ and $0.3333$
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