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## Homework Statement

Solve the differential equation.

[itex]\frac{dy}{dx}[/itex] = [itex]\frac{1}{xy}[/itex] + [itex]\frac{y}{x}[/itex]

## The Attempt at a Solution

[itex]\frac{dy}{dx}[/itex] = [itex]\frac{x + xy^{2}}{x^{2}y}[/itex]

[itex]\frac{dy}{dx}[/itex] = ([itex]\frac{x}{x^{2}}[/itex])([itex]\frac{1 + y^{2}}{y}[/itex])

([itex]\frac{y}{1 + y^{2}}[/itex])dy = [itex]\frac{x}{x^{2}}[/itex]dx

[itex]\oint\frac{y}{1 + y^{2}}[/itex]dy = [itex]\oint\frac{x}{x^{2}}[/itex]dx

I can't seem to get any further than there

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