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Differential EquationsChallengeNonhomogeneous Equations & Resonance

Nonhomogeneous Equations & Resonance · Challenge problem

The third-order equation y(3)−y′′−y′+y=8et+4e−ty^{(3)}-y''-y'+y=8e^{t}+4e^{-t} has a particular solution of the form yp=At2et+Bte−ty_p=At^2e^{t}+Bte^{-t}. Find yp(1)y_p(1).