what is the general form of an nth order linear differential equation with constant coefficient?

my notes says it's $$\large (A_n D^n + A_{n-1} D^{n-1} + \cdots + A_n)y = R(x)$$

but a quiz i secretly acquired says it's $$\large (A_o D^n + A_1 D^{n-1} + \cdots + A_{n-1} D + A_n)y = R(x)$$

so which one is right?

Question

what is the general form of an nth order linear differential equation with constant coefficient?

my notes says it's $$\large (A_n D^n + A_{n-1} D^{n-1} + \cdots + A_n)y = R(x)$$

but a quiz i secretly acquired says it's $$\large (A_o D^n + A_1 D^{n-1} + \cdots + A_{n-1} D + A_n)y = R(x)$$

so which one is right?

anonymous · Answer

first one is  An  An-1 .........  A0  i think ha?

lgbasallote · Answer

heh?

lgbasallote · Answer

yeah i think..i may have copied it wrong

anonymous · Answer

anyway those are constants it does'nt matter how to place them (any order is correct) 

so both are correct

lgbasallote · Answer

really? so what will be the wrong equation? can you give a sample?

anonymous · Answer

It is a notational problem. Both notations are OK.

lgbasallote · Answer

i think it would be nice to see a situation wherein it's wrong...so i;ll know when it's right..when it's wrong..

anonymous · Answer

there is no wrong situation...lol

lgbasallote · Answer

really? so it's always right?

lgbasallote · Answer

lol there must be a wrong situation :/

anonymous · Answer

Here are two representation of a general polynomial of degree 10
$$
p(x)=a(10) x^{10}+a(9) x^9+a(8) x^8+a(7)
   x^7+a(6) x^6+a(5) x^5+\a(4)
   x^4+a(3) x^3+a(2) x^2+a(1) x+a(0)$$

$$
 q(x)= a(0) x^{10}+a(1) x^9+a(2) x^8+a(3)
   x^7+a(4) x^6+\a(5) x^5+a(6)
   x^4+a(7) x^3+a(8) x^2+a(9)
   x+a(10)

$$