# Differential equation and fluids

1. Feb 25, 2008

### Niles

1. The problem statement, all variables and given/known data
Hi guys

Please take a look at the second question in 10.20 (the question with the diff. equation):

I have found the expression for the operator E, but how do I show that f(r) satiesfies the diff. equation?

3. The attempt at a solution

First thing would be to insert "psi"(r,theta) in E - but where to go from here? I am very lost.

Niles, It would be nice if you showed the work done for obtaining the differential operator E. It is not explicitly given in your link and I have no clue whether my result is correct or not. At a certain point in time I was pressed with my nose against the screen trying to read the link because the thing does not zoom in properly. It's a fairly bad reading link. It would help to post the question in it's entire form and also to show some of your work. Principally it is just applying the operator twice to the stream function and the equation you get then has the proposed solution $$\Psi(r,\theta)=f(r)\cdot sin^2(\theta)$$. The only thing to do is to put it in the equation and you will arrive at the required ordinary differential equation. As stated, I can't check anything over here because I don't have the book and it seems it is a rather lengthy algebraic journey, which I will undertake to help you, but I need to make sure that my operator is correct.