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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.

Thanks!

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    It's obvious: 4$2$.2011-01-08

1 Answers 1

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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.2011-01-08