- #1
Mastur
- 41
- 0
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,
v2ydy + vy2dv + y2sinvdv = 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.