A What is the significance of the constant m in the Hermite differential equation?

Mrinmoy Naskar
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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??
 
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Mrinmoy Naskar said:
y" - 2xy' + ny = 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??

please explain what is 'm'?
 
drvrm said:
please explain what is 'm'?
sorry for the confusion.. I made the correction in my qus...
 
Mrinmoy Naskar said:
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??
Several web pages that I looked at say that m is usually a nonnegative integer. Did you try searching for yourself?
 
Mrinmoy Naskar said:
can anyone tell me what kind of conts is m?? what is the suitable value of m??

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)
 
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Mark44 said:
Several web pages that I looked at say that m is usually a nonnegative integer. Did you try searching for yourself?
@mrinmoy Pl. see a detail analysis
in < http://www.ncl.ac.uk/maths/students/teaching/notebooks/SeriesSolnNotebook.pdf>
 
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Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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