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Math Help - simple differential equation

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by kuntah View Post
    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
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  3. #3
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    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..?
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