** Final answer to the problem

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** Step-by-step Solution **

** How should I solve this problem?

- Separable Differential Equation
- Exact Differential Equation
- Linear Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
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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 $2$

Simplify the fraction $3\left(\frac{y^{3}}{3}\right)$

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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 $n=1$

Multiply the fraction and term in $2\cdot \left(\frac{1}{2}\right)x^2$

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

Raise both sides of the equation to the exponent $\frac{1}{3}$

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

** Final answer to the problem

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