Method of Undetermined Coefficients

#math/2c03

Used to find particular solution to non-homogenous, linear, constant coefficient ODE $L[y]=g(x)$ when $g(x)$ is linear combination of functions of the form

where $\alpha ,\beta ,\gamma ,\delta$ are real numbers.

If $g(x)$ is a polynomial, then $\alpha =\beta =\gamma =\delta =0$.
If $g(x)=(polynomial)e^{\alpha x}$, then $\beta =\gamma =\delta =0,\alpha \ne 0$
If $g(x)=(polynomial)e^{\alpha x}\cos (\beta x))+(polynomial)(e^{\gamma x}\sin (\delta x)),\alpha ,\beta ,\gamma ,\delta \ne 0$