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I'm trying to find the general solution to

$$\frac{\text{d}y}{\text{d}x} = \frac{y-x^2}{\sin y-x}$$

Any ideas would be greatly appreciated.


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It's obvious: 42. – Mateen Ulhaq Jan 8 '11 at 0:29

Your equation is exact once you write it as $$f(x,y)\,\mathrm d x+g(x,y)\,\mathrm d y=0.$$ Find a potential, and voilà. I'll leave you the fun of doing that; the general solution is implictly defined by the equation $$\frac{x^3}{3}-xy-\cos y=c$$ with $c$ a constant.

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Thank you! I understand your answer. – user5498 Jan 8 '11 at 0:33

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