# Keep calm and solve this....

Calculus Level 5

$\large u = \csc^{-1}\large \sqrt{\dfrac{\sqrt{x}+ \sqrt{y}}{\sqrt[3]{x} + \sqrt[3]{y}}}$

$\large x^2\dfrac{\partial^{2}u}{\partial x^{2}} + 2xy\dfrac{\partial^{2}u }{\partial x\partial y} +y^{2}\dfrac{\partial^{2} u}{\partial y^{2}} =\dfrac{\tan u(b+ \tan^2 u)}{a^2}$

Find $$a+b$$, where $$a$$ and $$b$$ are coprime positive integers.

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