# Differential operator

1. Nov 11, 2005

### asdf1

for the following question:
[4(x^2)(D^2)+12xD+3)]y=0

my problem:
i only know how to solve this type of question if i change it back to its original form. however, if i want to solve it by just using D, how would i do that?

2. Nov 12, 2005

### quasar987

What do you mean its original form?

And what are you expected to do with this equation anyway?

3. Nov 12, 2005

### asdf1

i mean that if i changed the D to y

4. Nov 12, 2005

### quasar987

OH! Well I guess just treat Dy as dy/dx and solve as you would.

5. Nov 12, 2005

### saltydog

I looked at it early this morning and even briefly posted what I though was the factored form of the differential operators and even though it resulted in a correct answer, my factored version was incorrect because the differential operators are NOT commutative. Turns out equations with functions of x are not easily factored for this reason, something I'm not clear on. So I would just treat it as a regular Euler-Cauchy equation and look for a solution of the form:

$$y=x^{m}$$

(unless someone can further comment about the factoring).

Last edited: Nov 12, 2005
6. Nov 13, 2005

### asdf1

i had the same problem as you when i tried to factor it too~

7. Nov 14, 2005

### Harmeet Singh

This ia a quadratic in D.Just find out D using the formula used for quadratic equations and then proceed

8. Nov 14, 2005

### HallsofIvy

Staff Emeritus
The whole point is that this is an equation with VARIABLE coefficients. That method doesn't work with variable coefficients.

9. Nov 14, 2005

### asdf1

@@ why doesn't it work for variable coefficients?