Differential Equations - re-arrange?

[mrmonkah]

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

 

[Mark44]

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.

 

[LCKurtz]

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?

 

[mrmonkah]

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...

 

[Mark44]

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?