Differential equations- simultaneous equations

Jenkz
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Homework Statement



http://img228.imageshack.us/i/cimg5162f.jpg/

This isn't the usual format, so I hope it's still ok. It's just easier than writing it out on here. I can't work out how to form a simultaneous equation from (1) and (2).

When solved it should form the du/dx and dv/dx answers written.

The Attempt at a Solution



I have tried to work backwards from the answers, but I still can't figure it out. I've also tried re-arranging (1) to find du/dx or dv/dx and subbing into (2) and trying to re-arrange, but I can't get the answers either.

Help please?
 
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Nevermind, I've got it now. Just a stupid mistake.
 
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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