Hi, can anyone give me some direction how I would about solving this problem?

Thanks anyone that can help!

Attachment 20164

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- Dec 20th 2010, 12:33 PMjohn1990Need help solving differential equation
Hi, can anyone give me some direction how I would about solving this problem?

Thanks anyone that can help!

Attachment 20164 - Dec 20th 2010, 02:35 PMark600
The notation may be making the problem more complicated than it appears??:

I don't think you need to know anything more than $\displaystyle \frac{d}{dx}ax^n = anx^{n-1}$ - Dec 20th 2010, 02:46 PMark600
Using induction may make things easier too.

I've not gone through any calculations, but induction would be my first stab at this. - Dec 25th 2010, 08:37 PMSammyS
Here is an image from your attachment:

http://usera.ImageCave.com/DGSamSnyder/BitMap1.jpg(The $\displaystyle \displaystyle \alpha_i$ are real coefficients.)

I think there is a typo in the expression on the right-hand side of the equation.

$\displaystyle \displaystyle {{d}\over{dz}}\sum_{i=0}^n{{\alpha_i z^i}\over{i!}}$

$\displaystyle \displaystyle = {{d}\over{dz}}\alpha_0+\sum_{i=1}^n{{d}\over{dz}}{ {\alpha_i z^i}\over{i!}}$

$\displaystyle \displaystyle =0+\sum_{i=1}^n{{(i)\alpha_i z^{(i-1)}}\over{(i)(i-1)!}}$

$\displaystyle \displaystyle =\sum_{i=0}^{n-1}{{\alpha_{i+1} z^{i}}\over{i!}}$

- Dec 26th 2010, 01:14 PMjohn1990