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2
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finding weak form of nonlinear differential equation for FEM simulation
First notice that
$$
(k_3 - k_1)\sin(u)\cos(u)(u')^2 + (k_1\cos^2(u) + k_3\sin^2(u))u'' = ((k_1\cos^2(u) + k_3\sin^2(u))u')' + (k_1 - k_3)\sin(u)\cos(u)(u')^2.
$$
I choose to rearrange our equation so …