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Aug 6, 2017 at 11:37 history edited assaferan CC BY-SA 3.0
correction - added inversion.
Aug 4, 2017 at 10:57 comment added Nemo I think this is wrong. $$ydx + (6x^2 - \frac{g_2}{2})dy=y^2d\theta+(6x^2 - \frac{g_2}{2})^2d\theta=\\=\left(4x^3-g_2x-g_3+36x^4-6g_2x^2+g_2^2/4\right)d\theta\neq const\cdot d\theta.$$ However if $g_2=0$ then $ydx-\frac23 xdy=-g_3d\theta$.
Aug 3, 2017 at 16:21 comment added user1337 It looks like you took $g_3$ as a constant here. Do you know anything about the case where $g_3=4x^3-g_2x-y^2$, as in the end of my question?
Aug 3, 2017 at 11:48 history answered assaferan CC BY-SA 3.0