# Thread: Need help solving differential equation

1. ## Need help solving differential equation

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

Thanks anyone that can help!

2. The notation may be making the problem more complicated than it appears??:
I don't think you need to know anything more than $\frac{d}{dx}ax^n = anx^{n-1}$

3. Using induction may make things easier too.
I've not gone through any calculations, but induction would be my first stab at this.

4. Originally Posted by john1990
Hi, can anyone give me some direction how I would about solving this problem?

Thanks anyone that can help!

Here is an image from your attachment:
(The $\displaystyle \alpha_i$ are real coefficients.)

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

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

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

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

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

5. Originally Posted by SammyS
Here is an image from your attachment:
(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.