# Help with frobenius series

1. May 13, 2009

### rapwaydown

the question is
" find two linearly independent of frebenius series solutions for 4xy''+2y'+y=0"

I try almost everything to slove this, but could't figure it
any help is appercaited

thank you

2. May 13, 2009

### HallsofIvy

Staff Emeritus
Well, what have you done on it? You say you've tried "almost everything". Okay, what have you tried?

3. May 13, 2009

### rapwaydown

well, i divided the whole thing by 4x, trying to get it to the general format, but it didnt work out.

4. May 14, 2009

### HallsofIvy

Staff Emeritus
In other words, you really haven't done anything!

Start by writing
$$y= \sum_{n=0}^\infty a_n x^{n+c}$$
Find y' and y" from that and put them into the equation. What do you get?

5. May 14, 2009

### rapwaydown

i dont know how to find y' and y''
im slef learning def.Q

6. May 14, 2009

### rapwaydown

by the way, i dont think y' and y'' is needed here
i divided the whole thing by 4x, then slove for the indicial,
which are r=0,-.5
but i dont know what to do from this point on,
i think i need to find the eqution for cn, but dont know how.
can you help

7. May 16, 2009

### femi

You have to assume a solution as you have been advised
You dont need to divide by 4x.
When you assume the solution you will find d second and first derivatives of y, you will then subtitute into the equation.
I solved it and that's the way it goes.

8. May 16, 2009

### coomast

Though not the question it is interesting to know that this DE has a solution in closed form. One can find this by substituting $x=t^2$ in the equation. A very simple DE will appear and can be solved directly. Doing the inverse substituting on this solution gives the result of the original DE. This solution can then be compared to the series solution.

9. May 16, 2009

### HallsofIvy

Staff Emeritus
It's probably not a good idea to try to learn differential equations, by your self or not, if you do not know Calculus!

Are you seriously saying that you do not know how to find the derivatives of xn?

And, to even attempt a problem like this you should have had enough Calculus to know that a power series is "term by term" differentiable inside its radius of convergence.