4zy''+2y'+y=0

find series solution about z=0 and identify these solution in closed form

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- May 29th 2008, 10:17 AMszpengchaosolve differential equation by series
4zy''+2y'+y=0

find series solution about z=0 and identify these solution in closed form - May 29th 2008, 11:39 AMThePerfectHacker
If you divide through by x you get . The coefficient function for is Laurent series of order and same for . This means the equation is solvable through Frobenius method. The Frobenius equation would be so . These do not differ by integers so you can solve this equation on by letting where . For each value you will get a new linearly independent solution.

- May 29th 2008, 11:40 AMMoo
Hello,

Let

You will have to determine ~

Putting all the powers to , by changing the indices ~

In the first and second ones, n-1 becomes n. Then the series will start at 1 and 0..

Now, starting the series at the same point :

Therefore :

-->

And :

Find the induction formula :p