Question

QUESTION 3 Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used on y"+y=t+t sin(t).

Answer 1

+ Dy= dy dt The auxilary equ y"+yattt sint Cortdy=t+t sint where m+1=0 => m=i,-i The complementary Penebion CF = a cost +6 sunt where a&6 are constant. Corresponding to the special form it, we choose trail solution for pl as G + Cat Since sint occurs in the CF como orresponding to a root of ruitiplicity one, so the corresponding frail solution for Pi is Cst sint teat" Cost & Cotsint & &t cost Here Esent +Cq cost is not Included as it already appear in Of with arbitrary Coffcant, ado Theufore the suitable form of trail solution yct) is [Y(t) = Citlatt Czt sint & Cat Cost & Etsint tot cost CS Scanned with CamScanner