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## Homework Statement

[itex]xdx+sin\frac{y}{x}(ydx-xdy) = 0[/itex]

## The Attempt at a Solution

Well, it's quite easy. But I'm quite confused if this is homogeneous or not, because of the sine function. This is my solution, assuming that this is a homogeneous equation.

let x = vy, dx = vdy + ydv; then substituting these values in the equation gives me,

v

^{2}ydy + vy

^{2}dv + y

^{2}sinvdv = 0. The variables now are separable.

[itex]\frac{dy}{y} + \frac{dv}{v} + \frac{sinv}{v^2}dv = 0[/itex]

[itex]ln{x} + ln{v} + \int\frac{sinv}{v^2}dv = 0[/itex]

Now, I cannot integrate the last function. I still have a lot of problems to solve, and a lot of questions to ask. I'll post others later as soon as I have tried solving them.