# Separable differential equation, ex2 | Summary and Q&A

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March 16, 2015
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Separable differential equation, ex2

## TL;DR

Learn how to solve a differential equation by separating variables and integrating.

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### Q: What is the goal in solving this differential equation?

The goal is to rearrange the equation so that all the terms containing x and dx are on one side, while the terms with y and dy are on the other side.

### Q: How does multiplying both sides by dx help in rearranging the equation?

Multiplying both sides by dx cancels out the dx term on the left side, allowing it to be moved to the right side of the equation.

### Q: What are the next steps after rearranging the equation?

The next step is to integrate both sides of the equation, which involves finding the antiderivatives of the respective terms.

### Q: How is the final solution obtained?

By isolating the variable y, the cube root of the expression 3x + 3ln|x| is taken. The solution is then written as y = (3x + 3ln|x|)^(1/3) + K, where K represents a constant.

## Summary & Key Takeaways

• The content explains the process of solving a differential equation by separating variables and integrating.

• By dividing both sides by x and moving the dx term to the other side, the equation is rearranged.

• Integrating both sides allows for isolating the variable and finding the solution.