# A Hermite differential equation

1. Mar 20, 2016

y" - 2xy' + my = 0 this is well known hermite diff eqn. now can anyone tell me what kind of conts is m?? what is the suitable value of m??

Last edited: Mar 20, 2016
2. Mar 20, 2016

### drvrm

3. Mar 20, 2016

sorry for the confusion.. I made the correction in my qus...

4. Mar 20, 2016

### Staff: Mentor

Several web pages that I looked at say that m is usually a nonnegative integer. Did you try searching for yourself?

5. Mar 20, 2016

### drvrm

This is Hermite’s equation, where special choices of m give rise to the Hermite polynomials.
there exists a polynomial solution of the original equation whenever m = 2n , n = 0,1,2 , , , ... . With the choice m = 2n , and the arbitrary multiplicative constant chosen so that the coefficient of the term x^n is 2^(m/2)

6. Mar 20, 2016

### drvrm

@mrinmoy Pl. see a detail analysis
in < http://www.ncl.ac.uk/maths/students/teaching/notebooks/SeriesSolnNotebook.pdf> [Broken]

Last edited by a moderator: May 7, 2017