Differential Equations - re-arrange?

In summary, the problem is to solve the differential equation x dx = y^2 dy and find its solutions. This involves using techniques for solving differential equations and applying the chain rule to differentiate functions of x and y.
  • #1
mrmonkah
24
0

Homework Statement



So i am to differentiate: x dx = y^2 dy

The Attempt at a Solution



Am i right in thinking that i just do a simple re-arrangement to get: dx/dy = y^2/x and then differentiate this?

I am unfamiliar with having to differentiate when both x and y are present in the equation. Any help will be much appreciated.

Dan
 
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  • #2
Is the object to find d2y/dx2? If so, solve for dy/dx, and then differentiate implicitly. That is, you differentiate x and functions of x alone as you normally would, but differentiate y and functions of y alone as if they were (implicitly) functions of x. You need to use the chain rule to do this.

For example, d/dx(y2) = 2y * dy/dx.
 
  • #3
Your problem statement is confusing. Do you really mean differentiate? And if so, with respect to which variable? Or are you trying to solve a differential equation by using separation of variables and integrating?
 
  • #4
The question literally says: Solve The Following - x dx = y^2 dy, appologies for been unclear, but that is the very problem i have with the question i do not understand what is being asked for. I thought that there was perhaps something obvious to do with the equation...
 
  • #5
That's what we were looking for, the literal statement of the problem.

By "solve" it means find the solutions of the differential equation. It did not say to differentiate something.

Do you know of any techniques for solving differential equations?
 

1. What is the purpose of re-arranging differential equations?

Re-arranging differential equations allows us to solve for different variables and understand the relationships between them. It also helps to simplify complex equations and make them easier to work with.

2. How do you re-arrange a differential equation?

To re-arrange a differential equation, we need to isolate the variable we want to solve for on one side of the equation and move all other terms to the other side. We can then use algebraic manipulation and integration techniques to solve for the variable.

3. Can re-arranging a differential equation change its solution?

Yes, re-arranging a differential equation can change its solution. This is because the process of re-arranging can introduce new terms or manipulate existing ones, which can alter the overall solution of the equation.

4. When is it necessary to re-arrange a differential equation?

It is necessary to re-arrange a differential equation when we want to solve for a specific variable or when the equation is too complex to solve in its original form. Re-arranging can also help us to better understand the behavior of the system described by the equation.

5. Are there any limitations to re-arranging differential equations?

Yes, there are limitations to re-arranging differential equations. In some cases, the equation may not be able to be re-arranged in a way that makes it solvable. Additionally, re-arranging can sometimes introduce extraneous solutions, so it is important to check the validity of the solution after re-arranging.

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