Solve the recurrence relation of an+4 + 2an+2 + an=0, n greater than or equal to zero .
Solution. The characteristic equation has the form
Let y=λ2. As a result, we get the quadratic equation
"(y+1)^2=0"
The solution to this equation
Back to substitution
"\\lambda^2=-1"
As result
and
The solution to the equation can be represented as
where C1, C2, C3 and C4 are constants.
Answer.
"a_n=(C_1+nC_2)(-i)^n+(C_3+nC_4)i^n"where C1, C2, C3 and C4 are constants.
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