Stumped? Need Help with PDE Problem - Sarah Needs a Hand!

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hmmm i have no idea where to even start with this problem, i cannot find any examples that are similar or anything like that anywhere!

http://img147.imageshack.us/img147/2319/picture18ur9.png

anyone got an idea as to a good first step to take?

thanks

sarah :)

edit: i tryed something wild and came up with http://img470.imageshack.us/img470/7415/picture22tm5.png but i didnt use any knowlage of PDE's to work that out...hmmm... :S
 
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sarahisme said:
hmmm i have no idea where to even start with this problem, i cannot find any examples that are similar or anything like that anywhere!

http://img147.imageshack.us/img147/2319/picture18ur9.png

anyone got an idea as to a good first step to take?

thanks

sarah :)

edit: i tryed something wild and came up with http://img470.imageshack.us/img470/7415/picture22tm5.png but i didnt use any knowlage of PDE's to work that out...hmmm... :S

how did you get your answer??
 
Last edited by a moderator:
stunner5000pt said:
how did you get your answer??
i just differentiated u(x,y) with respect to x then respect to y and that gave me A(u)

but doesn't that seem to simple? i mean, there is no PDE stuff involved really... :S
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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