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$(2xy + 3y^2)dx + (x^2 + 6xy - 2y)dy = 0$ $y(1) = -1/2$

How do you solve this? I have just started learning Differential equations and I have some trouble.

Is this equivalent with this?

$2y + (6x - 2) = 0$ $y(1) = -1/2$

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    See [here](http://math.stackexchange.com/questions/215324/proof-for-exact-differential-equations-shortcut/215346#215346).2012-12-13

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You can rewrite your equation as $ df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy = 0, $ where $df$ is the total differential of a function $f\left(x,y\right)$ that you should determine. Then $df = 0$ implies $f\left(x,y\right)$ is a constant. Determine this constant with the condition on $y\left(1\right)$.