1. ## 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

2. 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

$2a_2 + a_0 = 0~\wedge~a_0 = 0~\implies~2a_2 + 0 = 0~\implies~2a_2 = 0 ~\implies~a_2=0$

3. 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..?