Need help solving differential equation

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December 20th 2010, 12:33 PM
john1990

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Need 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
December 20th 2010, 02:35 PM
ark600

The notation may be making the problem more complicated than it appears??:
I don't think you need to know anything more than $\frac{d}{dx}ax^n = anx^{n-1}$
December 20th 2010, 02:46 PM
ark600

Using induction may make things easier too.
I've not gone through any calculations, but induction would be my first stab at this.
December 25th 2010, 08:37 PM
SammyS

Quote:

Originally Posted by john1990

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

Thanks anyone that can help!

Attachment 20164

Here is an image from your attachment:
http://usera.ImageCave.com/DGSamSnyder/BitMap1.jpg(The $\displaystyle \alpha_i$ are real coefficients.)

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

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

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

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

$\displaystyle =\sum_{i=0}^{n-1}{{\alpha_{i+1} z^{i}}\over{i!}}$
December 26th 2010, 01:14 PM
john1990

Quote:

Originally Posted by SammyS

Here is an image from your attachment:
http://usera.ImageCave.com/DGSamSnyder/BitMap1.jpg(The $\displaystyle \alpha_i$ are real coefficients.)

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

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

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

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

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

Hi, ye I see that. Ha, what a dummy I am! Should have seen that.

Cheers.