In effect the advantage of having introduced the arbitrary coefficient
bois that it can be defined in order to make even the first order term negligible with respect to the constant term, whence the notation reported here; so, neglecting all powers of i, the right hand side reduces to a constant.
However, for polynomials of degree five or higher with arbitrary coefficients
, the Abel-Ruffini theorem states that there is no algebraic solution.
A specific solution is obtained when initial conditions, or boundary conditions, are used to evaluate the arbitrary coefficients
in the linear combination of homogeneous solutions.
The analytical results depend upon inclusion of arbitrary coefficients
based on experimental data to accurately predict performance.
where a, b, c are arbitrary coefficients
with a [not equal to] 0, b [not equal to] 0.