Solved example of first order 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
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 $\int4ydy$ 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
Apply 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 $\int5x^2dx$ and replace the result in the differential equation
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration
Divide both sides of the equation by $2$
Applying the power of a power property
Removing the variable's exponent
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