Method of Undetermined Coefficients (Particular Integral)

Rarely Tested
For specific $$R(x)$$ forms:
  • $$R(x) = e^{kx}$$: Assume $$y_p = Ae^{kx}$$ (unless $$k$$ is root of AE)
  • $$R(x) = \sin(px)$$ or $$\cos(px)$$: Assume $$y_p = A \cos(px) + B \sin(px)$$
  • $$R(x) = x^n$$: Assume $$y_p = a_0 + a_1x + \dots + a_nx^n$$
Adjust if overlap with complementary solution.
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