Answer Happy

Given y(4)−9y′′′−81y′′+729y′=t2+2+tsint determine a suitable form for Y(t) if the method of undetermined coefficients is towbe used. Do not evaluate the constants. A suitable form of Y(t) is: Y(t)=
A0​t2+A1​t+A2​+(B0​+B1​t)cost+(C0​+C1​t)sint t(A0​t+A1​)+B0​cost+C0​sint t(A0​t2+A1​t+A2​)+B0​tcost+C0​tsint (A0​t2+A1​t+A2​)+(B0​+B1​t)cost+(C0​+C1​t)sint t(A0​t+A1​)+(B0​+B1​t)cost+(C0​+C1​t)sint A0​t2+A1​t+A2​+B0​cost+C0​sint t(A0​t2+A1​t)+B0​cost+(C0​+C1​t)sint A0​t+A1​+B0​tcost+C0​tsint