question archive Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation
Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation
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Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y" + 9y = 16t sin 3t The root(s) of the auxiliary equation associated with the given differential equation is/are 3/, - 3 / (Use a comma to separate answers as needed.) Write the form of a particular solution. Choose the correct answer below. O A. yp(t) = (Agt# + Ants + A, 12 + Apt) et cos 3t+ (Bat4 + B2+3 + Bit? + Bo) el sin 3t O B. yp(t) = t( Agt3 + A2(2 + Ant+ Ap) et cos 3t+t(Bat3 + B2+2 + Bit + Bo) et sin 3t O c. yp(t) = (Agt3 + Ant2 + Ant+ Ao) cos 31+ (Bat3 + B2(2 + Byt+ Bo) sin 3t O D. yp(t) = t(At3 + Act2 + Ant + Ap) cos 3t +t(B3+3 + B2+2 + Bit+Bo) sin 3t
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Roots of Auxiliary equation associated with the given differential equation are 3i, -3i
Option (C) is correct
Step-by-step explanation
Q yl + 9 4 = 16 + sen( 3 t ) A-E : - m 2 + 9 = 0 m 2 = - 9 m = 1 3i Roots of the auxilliany ean associated with the genen diff eq"? are 31. - 31 Form of a particular soin !- ( ) yputs = ( Ast + Aztta, t + Ao ) los3t + ( B3 t 's + B 2 1 + Bit + Bo) Sin3t option (@ is correct.
