Method of undetermined coefficients
= Method of undetermined coefficients
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Choose a finite trial family of polynomial-exponential or trigonometric functions for a <particular solution>, substitute it into a constant-coefficient linear equation, and solve for its coefficients. If the forcing exponent is a characteristic root of multiplicity $m$, multiply the ordinary trial by $t^m$ to leave the homogeneous <kernel>. The method is efficient for forcing families preserved by differentiation.