Can we get a tricky differential equations thread going? ODEs

>>8584799
I hate numbers so much

[eqn]
\left[r^2 \partial_r^2 + r \left({3\over \ln r}-2 i \cot\theta \right) \partial_r + \partial_\theta^2 + i\left({3\over \ln r}-2 i \cot\theta - 1 \right)\partial_\theta\right]\,F(r, \theta) = A\, F(r,\theta)
[/eqn]
[math] A [/math] is constant and [math] r [/math] and [math] \theta [/math] are on the unit disk.

For those of you who think you can solve it on the first go - think again.

>>8584805
how do you get the LaTeX/MathML on here?

>>8584810
sandwich between "[math]" and "[/math]" in text and "[eq]" and "[/eq]" for equation block.

>>8584812
Okay well that didn't work lol. The first one is the word math between brackets [ ] to open and /math in brackets to close. The second one was typed wrong, which is why it actually rendered correctly. It should be "eqn". Anyways lets focus on the diff eq.

>>8584822
[math] 2/3 /math

>>8584830
[math 2_3 /math]

>>8584822
fuck I'm retarded

>>8584799
For [math]f:{\mathbb{R}^n} \to \mathbb{R}[/math] solve [math]\sum\limits_{i = 1}^n {\prod\limits_{j = 1}^{Graham} {\frac{{{\partial ^j}f}}{{\partial {x_i}^j}}} } = 0[/math]