# Solving a Partial Differential Equation

1. Apr 21, 2012

### the0

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

Find functions y=y(x) defined on (-∞,0) or (0,+∞) which verify:

xy'+(x2-1)cot(y)=0,
y($x_0{}$)=$y_0{}$ for $x_0{}$≠0 and cos($y_0{}$)≠0

3. The attempt at a solution

I'm really stuck on this one!
Any help will be very much appreciated!

Last edited: Apr 21, 2012
2. Apr 21, 2012

### tiny-tim

welcome to pf!

hi the0! welcome to pf!

hint: separation of variables?

3. Apr 21, 2012

### the0

Ok, thanks!
So I get:

xy' = (1-2x2)cot(y)

y'tan(y) = (1-2x2)/x

Then how do I go about integrating the left hand side?

4. Apr 21, 2012

### tiny-tim

(where did that 2 come from? )

easier if you write it with d's …

tan(y) dy = (1-x2)/x dx

5. Apr 21, 2012

### the0

I realised that it was that simple right after I posted it haha
and I missed out the 2 in the original statement of the problem, my mistake, sorry about that.
Thanks a lot!

6. Apr 21, 2012

### the0

I realised that it was that simple right after I posted it haha
and I missed out the 2 in the original statement of the problem, my mistake, sorry about that.
Thanks a lot!

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