First-order differential equation

  • Thread starter Mathematicsss
  • Start date
  • #1
Mathematicsss

Homework Statement


y'+tanxy=sinx

Homework Equations



integrating factor I(x)= exp{lnIsecxI}[/B]


The Attempt at a Solution


I have secxy= integral of sinx I(x)
I am not sure how to integrate that because secx is in absolute value form.[/B]
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722

Homework Statement


y'+tanxy=sinx

Homework Equations



integrating factor I(x)= exp{lnIsecxI}[/B]


The Attempt at a Solution


I have secxy= integral of sinx I(x)
I am not sure how to integrate that because secx is in absolute value form.[/B]

There are two cases: (1) the values of ##x## make ##\sec(x) > 0##; or (2) the values of ##x## make ##\sec(x) < 0##. Just analyze both cases, although you need to worry about whether the solution ##y(x)## can remain meaningful if ##x## crosses from one region to the other.
 

Related Threads on First-order differential equation

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
712
  • Last Post
Replies
2
Views
820
  • Last Post
Replies
6
Views
510
  • Last Post
Replies
2
Views
1K
Top