** Final Answer

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** Step-by-step Solution **

Problem to solve:

** Specify the solving method

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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 of the equality

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Integrate both sides of the differential equation, the left side with respect to $y$, and the right side with respect to $x$

The integral of a function times a constant ($3$) is equal to the constant times 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 number or constant function, such as $2$

Any expression multiplied by $1$ is equal to itself

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Solve the integral $\int3y^2dy$ and replace the result in the differential equation

The integral of a function times a constant ($2$) is equal to the constant times 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 number or constant function, in this case $n=1$

Any expression multiplied by $1$ is equal to itself

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

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Solve the integral $\int2xdx$ and replace the result in the differential equation

Removing the variable's exponent raising both sides of the equation to the power of $\frac{1}{3}$

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Find the explicit solution to the differential equation. We need to isolate the variable $y$

** Final Answer

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