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

[EtherealMonkey]

So, this is where I am stuck:

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

I am confrused...

 

[kosovtsov]

Do you think that

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

is better?

 

[dextercioby]

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

 

[HallsofIvy]

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

 

[annoymage]

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

 

[gato_]

kosovtsov just posted it...

 

[annoymage]

waw, lambert, i need to study that thing