# Homework Help: Separable D.E., Nonlinear in terms of y(x) after integration

1. Dec 15, 2009

### EtherealMonkey

So, this is where I am stuck:

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

I am confrused...

2. Dec 15, 2009

### kosovtsov

Do you think that

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

is better?

Last edited by a moderator: Dec 16, 2009
3. Dec 15, 2009

### dextercioby

It's easier to express <x> in terms of <y>, wouldn't you say ?

4. Dec 16, 2009

### HallsofIvy

EtherealMonkey, are you required to solve for y? That isn't always necessary or possible.

5. Dec 16, 2009

### annoymage

hmm, but is it possible to make an explicit form in terms of x?

6. Dec 16, 2009

### gato_

kosovtsov just posted it....

7. Dec 16, 2009

### annoymage

waw, lambert, i need to study that thing