[SOLVED] Swapping your dependent/independent variables? (ODE)
I just discovered this board and it seems like an awesome idea. I have a question that I've been wracking my brains on for a while now and I can't find any answers from any other online sources so I was hoping that asking real people would help =).
I have a question set that goes like this:
Solve the following equations by regarding y as the independent variable rather than x
and an example of one of the questions is:
(1-4xy^2)dy/dx = y^3.
Now, how do you swap the dependent/independent variables?
Is the differential equation the same as
(1-4xy^2) = y^3(dx/dy)?
i.e., is dy/dx*dx/dy = 1?