- #1
Saladsamurai
- 3,020
- 7
Homework Statement
So I have a problem in which I have arrived at the following equation (which according to my professor is correct). I am having some trouble with the math now:
[tex]
\int_0^x \left [ 1 - \left ( \frac{\xi}{x} \right )^{3/4} \right ]^{-1/3}
\frac{dT_w}{d\xi}\,d\xi = C \qquad(1)
[/tex]
Where C is a big lump of constants. I was then told to assume that Tw is given by a power series:
[tex]
T_w (\xi) = \sum_0^\infty a_n\xi^n\qquad(2)
[/tex]
Plugging (2) back into (1) gives:
[tex]
\int_0^x \left [ 1 - \left ( \frac{\xi}{x} \right )^{3/4} \right ]^{-1/3}\sum_{n=0}^\infty na_n\xi^{n-1}\,d\xi = C \qquad(3)
[/tex]
Somehow, I am supposed to get from (3) that Tw is a constant by solving for the an's.
I am not really sure how to handle (3) mathematically? Can anyone offer up the next step?