# How to solve Differential equation

1. Oct 19, 2007

### giorgio_29

Hello!
How to solve this diff eq?

$$\ y'' + a$$$$\frac {y} {x}$$ $$\ +b$$$$\frac {y} {x^2}$$ $$\ = 0$$

2. Oct 19, 2007

### giorgio_29

Malmstén?

3. Oct 19, 2007

### AiRAVATA

ANSAT:

$$y(x)=\sum_{n=0}^\infty a_n x^n$$

4. Oct 19, 2007

### giorgio_29

yes Frobenius series for fuchsian points....., but Malmstén found the solution in term of modified Bessel functions, it is quite better.

5. Oct 19, 2007

### AiRAVATA

Then you need to transform such equation to look like the modified Bessel equation.

6. Oct 19, 2007

### giorgio_29

yes yes

the transformations are in the Watson book

the equation transform into a Bessel equation by using Malmstén transformations.

7. Oct 21, 2007

### AiRAVATA

Then what is the question?

8. Oct 22, 2007

### giorgio_29

after asking how to solve that equation I found the solution.

tks

gio