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

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EtherealMonkey
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So, this is where I am stuck:

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

I am confrused... :blushing:
 

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Do you think that

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

is better?
 
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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