• Support PF! Buy your school textbooks, materials and every day products Here!

Dif Eq x^2y' - cos (2y) = 1

  • Thread starter Icebreaker
  • Start date
  • #1
Icebreaker
How do I go about solving

x^2y' - cos (2y) = 1

This is unlike anything I've seen so far. Or so I think.
 
Last edited by a moderator:

Answers and Replies

  • #2
saltydog
Science Advisor
Homework Helper
1,582
2
Icebreaker said:
How do I go about solving

x^2y' + cos (2y) = 1

This is unlike anything I've seen so far. Or so I think.
It's separable right?
 
  • #3
lurflurf
Homework Helper
2,423
123
saltydog said:
It's separable right?
Yes
Trig is your friend.
as a matter of personal taste I enjoy the use of the identity
1-cos(2y)=2(sin(y/2))^2
 
  • #4
Icebreaker
Ok, I got it, thanks for the help.

I got y = arctan ( c = 2/x)
 
Last edited by a moderator:
  • #5
Icebreaker
18 down, 2 more to go:

y' = (4x + 2y - 1)^(1/2)

and

(1-xy)y' + y ^2 + 3xy^3 = 0

The last one kinda looks like Riccati, but I can't get it to work.


edit: I got the second one. One more ODE remains... I don't know how to approach that one.
 
Last edited by a moderator:
  • #6
saltydog
Science Advisor
Homework Helper
1,582
2
Icebreaker said:
18 down, 2 more to go:

y' = (4x + 2y - 1)^(1/2)

and

(1-xy)y' + y ^2 + 3xy^3 = 0

The last one kinda looks like Riccati, but I can't get it to work.


edit: I got the second one. One more ODE remains... I don't know how to approach that one.
Regarding:

[tex]\frac{dy}{dx}=\sqrt{4x+2y-1}[/tex]

How about squaring it for starters. Then let:

[tex]p=\frac{dy}{dx}[/tex]

Differentiate it to get an ODE in p. Then separate variables.
 

Related Threads for: Dif Eq x^2y' - cos (2y) = 1

Replies
6
Views
1K
  • Last Post
Replies
6
Views
2K
Replies
5
Views
4K
Replies
23
Views
2K
  • Last Post
Replies
5
Views
1K
Replies
4
Views
931
  • Last Post
Replies
6
Views
1K
Top