Here, we show you a step-by-step solved example of first order differential equations. This solution was automatically generated by our smart calculator:
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
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 ($4$) 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 $4\cdot \left(\frac{1}{2}\right)y^2$
Solve the integral $\int 4ydy$ and replace the result in the differential equation
The integral of a function times a constant ($5$) 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 $5\left(\frac{x^{3}}{3}\right)$
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
Solve the integral $\int 5x^2dx$ and replace the result in the differential equation
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