Solving xy'+(x²-1)cot(y)=0 with initial condition

Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
5 replies · 2K views
the0
Messages
14
Reaction score
0

Homework Statement



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

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

The Attempt at a Solution



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

Discussion

Physics news on Phys.org
welcome to pf!

hi the0! welcome to pf! :smile:

hint: separation of variables? :wink:
 
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?
 
the0 said:
y'tan(y) = (1-2x2)/x

(where did that 2 come from? :confused:)

easier if you write it with d's …

tan(y) dy = (1-x2)/x dx :smile:​
 
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!
 
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!