Separation of variables is a useful way to solve simple differential equations. It might seem tricky at first, but it's pretty easy once you learn how to do it.
First, you'll need to look at your equation. It usually looks something like this:
The goal is to get all the terms on one side of the equation and all the terms on the other side. You can rearrange the equation to look like this:
Next, it's time to integrate. This just means you need to find the integral (or the area under the curve) of both sides:
Now you have two separate integrals that you can work on one at a time. After you finish integrating, remember to add a constant to one side of the equation.
Finally, you can try to solve for in terms of , if it's possible. If not, that's okay too! You can just leave your answer in its implicit form.
Overall, once you separate the variables, it's all about applying what you learned. Happy solving!
Separation of variables is a useful way to solve simple differential equations. It might seem tricky at first, but it's pretty easy once you learn how to do it.
First, you'll need to look at your equation. It usually looks something like this:
The goal is to get all the terms on one side of the equation and all the terms on the other side. You can rearrange the equation to look like this:
Next, it's time to integrate. This just means you need to find the integral (or the area under the curve) of both sides:
Now you have two separate integrals that you can work on one at a time. After you finish integrating, remember to add a constant to one side of the equation.
Finally, you can try to solve for in terms of , if it's possible. If not, that's okay too! You can just leave your answer in its implicit form.
Overall, once you separate the variables, it's all about applying what you learned. Happy solving!