# Thread: power series method and frobenius method

1. ## power series method and frobenius method

I've got a differential equation : (x^2)y'' +(1+3x)y' +y=0 and have used frobenius method to turn it into a power series. that bit was fine, have

y=((n-1)(n-2)+3(n-1)+1)An-1 + nAn =0

problem is the question then says to find two linearly independent solutions, but i can only make it work to get one solution. because i have An and An-1 there is only 1 between them and for two solutions would been it to be something like An and An-2. Any suggestions??

Sarah

2. ...Check back with your textbook :P

The relation u have found for the A_n concerns only one of the two solutions. There is a specific formula for the other solution, if you are lucky it will be of the form $x^r\sum b_nx^n$, for suitable r. If not, there will be a logarithm involved (and that will require a lot of calculations).

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# difference between power series and frobenus series in ordinary differential equations

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