# Power series and differential equation

• May 16th 2007, 10:31 AM
totalnewbie
Power series and differential equation
I need to solve this for tomorrow surely but it causes to me headache.
• May 16th 2007, 11:38 AM
ThePerfectHacker
Why are you looking for a solution centered at x_0=1.
I did x_0=0 instead. I think it is easier.

Remember you need to find the "Cauchy Product"
• May 16th 2007, 12:10 PM
totalnewbie
Quote:

Originally Posted by ThePerfectHacker
Why are you looking for a solution centered at x_0=1.
I did x_0=0 instead. I think it is easier.

Remember you need to find the "Cauchy Product"

I actually don't understund what you mean by x_0=1 but I have to say that I did my half-done solution using my math book which uses the same approach. Although it is hard to figure out what the all solution means pictorially because the author of this book tried to explain the examples as briefly as possible.
I analyzed your solution and have to admit that I can't understand, how you get 3a3-b2=1.
How does the final answer look like ?
I am little bit confused.
• May 16th 2007, 01:00 PM
ThePerfectHacker
Quote:

Originally Posted by totalnewbie
I actually don't understund what you mean by x_0=1 but I have to say that I did my half-done solution using my math book which uses the same approach. Although it is hard to figure out what the all solution means pictorially because the author of this book tried to explain the examples as briefly as possible.
I analyzed your solution and have to admit that I can't understand, how you get 3a3-b2=1.
How does the final answer look like ?
I am little bit confused.

Because the right hand side is a power series of the form:
0+0x+1x^2+0x^3+0x^4+...
And the left hand side is also a power series.

The only way two power series can be equal only if each corresponding part is each.