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So I would like to get some input on the solution I came up with on the following problem:

enter image description here

There is obviously no way of finding an explicit solution (y= ...) using separation of variables like I did. So would it be correct to leave the answer like this?

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It's what you call an 'implicit solution'. Since an explicit solution isn't possible with elementary functions I think that's the only solution that could be accepted. Also, I uploaded a higher-contrast version of your picture. – anon Aug 29 '11 at 21:56
This sort of thing happens quite often. You have identified all curves $F(x,y,c)=0$ that satisfy the equation. Given initial conditions, you could find $c$. Really can't go any further, so this sort of answer would be perfectly acceptable. – André Nicolas Aug 29 '11 at 22:23
Maybe one of you could leave a (CW?) answer to settle this? – J. M. Aug 30 '11 at 2:15
Thanks all. Yeah leaving an actual answer would be a good idea – chaver Aug 30 '11 at 2:30
up vote 1 down vote accepted

Check your answer against Wolfram-Alpha.

enter image description here enter image description here enter image description here

and it appears you have it correct.

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