Driven Constant Coefficient Linear Differential Equations | MAT 2705, Study notes of Differential Equations

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driven constant coefficient linear DEs (methed of undetermined coefficients) yls dys dy = e%te™% | ylol=a, yo) =o CA CLAS ; (D440 + 4)y F(t) 15 thself a san of a const coeff linear hom DEY een eyrey S Carre) =o reagrt 4 =O ret vet O-y(p+) FH =O (42% =O cee (o-dn[O+2) Zum eke e* j Un= ¢ +x) e™ O-rCon)O+)>Y = O-DEH) CoE) SO home geneous soln. (COM (PF +2)% Fo 4th order HomDE , : 2 -\ Y= Yar¥p need to find = -2 aby particule soln Yp oultr aya, 4 -% ¥ “ Qe YS Ul err ertcuamje’™ +he™-e% Was Hi acath-l =O % coz H+2(9) as er = 3(3) g(ieme™ *+ ke +e WY soln Gmplicaton: Some ney roots coincide with some old cots ~% ym=ez, ylo=o 2x wey fy 4y= e +e 4 z reg TPR E-D(era =o (b-2 (P42) ( ete") =o (© +Z)*Yy same ze RP a 5 bho tx 2x nos -2Cor+e)(DeZ)ZyR oO} Ys GrCexregxeO + cae (6-2) Cr+z)3 = 0 ey Bertx ™ bee pang Yn Up = Caxte “Fqe nults 3 Pi nowbacesub Up inte onginal DE to delermne C3 ,¢¢; then sche ICS. * CHECK WITH dsdve