# 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...

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#### kosovtsov

Do you think that

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

is better?

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#### dextercioby

Homework Helper
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

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