# simple differential equation

• Dec 18th 2007, 11:55 AM
kuntah
simple differential equation
I don't understand one step in the following problem

Series Solutions to Second Order Linear Differential Equations

They say

Now we equate coefficients. The terms in the series begin with the first power of x, hence the constant term gives us
2a2 + a0 = 0

a0 = 0, but why is a2 equal to a0?

Why is this zero, and not something else?

Thanks very much
• Dec 18th 2007, 12:56 PM
earboth
Quote:

Originally Posted by kuntah
I don't understand one step in the following problem

Series Solutions to Second Order Linear Differential Equations

They say

Now we equate coefficients. The terms in the series begin with the first power of x, hence the constant term gives us
2a2 + a0 = 0

a0 = 0, but why is a2 equal to a0?

Why is this zero, and not something else?

Thanks very much

Hello,

if you have

$2a_2 + a_0 = 0~\wedge~a_0 = 0~\implies~2a_2 + 0 = 0~\implies~2a_2 = 0 ~\implies~a_2=0$
• Dec 18th 2007, 01:13 PM
kuntah
Yes i understand what you mean, but why is the whole expression zero?

So, why is
2a2 + a0 =0

and not for example 1, or 2..?