## Final Answer

## Step-by-step explanation

Problem to solve:

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 the sum of two or more functions is equal to the sum of their integrals

The integral of the sum of two or more functions is equal to the sum of their integrals

Solve the integral $\int2\left(y+1\right)dy$ and replace the result in the differential equation

The integral of a constant is equal to the constant times the integral's variable

The integral of a constant by a function is equal to the constant multiplied by the integral of the function

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 by $3$

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$