General Solutions for Trivial High Order PDEs

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I should find the general solution of the two following trivial PDEs.

<br /> u=u(x_1,x_2,...,x_n)<br />

1)

<br /> \frac{\partial u}{\partial x_1 \partial x_2} = 0<br />

2)

<br /> \frac{\partial u}{\partial x_1} - u = 0<br />
 
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What in particular are you having trouble with?
 
What have you tried? Per forum rules, you need to show some effort at solving the problem.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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