# Homework Help: Solving ode

1. Aug 13, 2010

### 01jbell

hey i am stuck on this question for my ode course its using frobunius

4. show that the equation

yii + 1/x yi + (1-1/(4*x^2))y = 0

has a regual point at x=0
using the method of frobenius assuming a solution of the form

y=$$\sum$$ ar xc+r

show that the idical equation is c^2=1/4

thanks for nay help given
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 13, 2010

### hunt_mat

What have you managed so far?

3. Aug 13, 2010

### 01jbell

i have proved that x=0 is a singular point and i rearanged the ode to get

x^2 yii + x y^i + x^2 y -1/4 y =0

however trying to work out coeff of xr , xr+1 etc etc is the probelm because i get

a0*(r^2-0.25) = 0
a1*{(r+1.5)*(r+0.5)}=0

and i thought u would have ot get a a0 in the equation for a1

4. Aug 13, 2010

### vela

Staff Emeritus
The r's in your equations should be c's, but otherwise they look okay.

If you solve for the coefficients for r≥2, you'll see they depend on the either a0 or a1.

5. Aug 13, 2010

### HallsofIvy

Because this 0 is a "regular singular point" for this problem, you cannot use the standard power series. You will have to use "Frobenious' method"- try something of the form
$$y= \sum_n a_nx^{n+c}$$

Choose c so that a0 is NOT 0.