Separable D.E., Nonlinear in terms of y(x) after integration

Click For Summary
The discussion revolves around the equation ln(y) + y² = sin(x) + c₀, with participants expressing confusion over solving for y. One user suggests that expressing y in terms of x using the Lambert W function could simplify the problem. There is a debate about whether it is necessary to solve explicitly for y, as it may not always be feasible. The mention of the Lambert W function indicates a need for further study on this topic. Overall, the conversation highlights the complexities of nonlinear equations and the potential utility of advanced mathematical functions in finding solutions.
EtherealMonkey
Messages
41
Reaction score
0
So, this is where I am stuck:

ln\left(y\right)+y^{2} = \sin{x}+c_{0}

I am confrused... :blushing:
 
Physics news on Phys.org
Do you think that

y(x) =\pm\sqrt{2LambertW(2exp(2sin(x)+C)}/2

is better?
 
Last edited by a moderator:
It's easier to express <x> in terms of <y>, wouldn't you say ?
 
EtherealMonkey, are you required to solve for y? That isn't always necessary or possible.
 
hmm, but is it possible to make an explicit form in terms of x?
 
kosovtsov just posted it...
 
waw, lambert, i need to study that thing
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 18 ·
Replies
18
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
Replies
4
Views
2K
Replies
19
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K