Solving a Partial Differential Equation

[the0]

Homework Statement

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

The Attempt at a Solution

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

 

[tiny-tim]

welcome to pf!

hi the0! welcome to pf!

hint: separation of variables?

 

[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?

 

[tiny-tim]

y'tan(y) = (1-2x²)/x

(where did that 2 come from? )

easier if you write it with d's …

tan(y) dy = (1-x²)/x dx ​

 

[the0]

I realized 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!

 

[the0]

I realized 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!