Ah yes, I stupidly made an assumption that on x and x + \mathrm{d}x edges, where y = const., the forces don't have the y component. I then tailored my derivation around this assumption.
If I now try it again.
Force on x and x + \mathrm{d}x edges is \gamma \sqrt{\mathrm{d}y^2 +...
Homework Statement
The Plateau equation (minimal surface of a soap film) can easily be derived from variational principle. We want to minimize the area of the soap film,
S = \int \sqrt{1 + z_x^2 + z_y^2} \, \mathrm{d}x \, \mathrm{d}y
,
and through Euler-Lagrange equation we get the...