Question

Problem 4 (12 points) Set-up the most appropriate form of an ansat for the particular solution () using the Method of Undetermined Cocflicients. Nood NOT find the values of these undetermined coeflicients. (a) y" 4y 12y = sin(21) (1) y = 2.25

Answer 1

a solution : - Given differential equation is y" - 44'-12y = = sin(at) Here corre corresponding to the special form sinat of right hand sides of o we choose trial solution for A sin(t) + B os (2) particular solution Up Hence Yose Asim (at) tВ cos (24) is the

solution Yp (2) are tezt 2 nequined ed appropriate form of the particular where A and B urde termined coefficients to be determined, (Any) by Given differential equetion is y" -&y' + 4y Here corresporting to special form trinat of Ripus.of ☺ we choose the trial solution for porticular solution Yp et (Ao & Aft) for method of render- mined coefficients. Hence et (Ao +A (4) where to and tet at Yp (+) = ane undetermined coefficients (constants) to be determind by given artial conditions is the appropriate form of particular solution. Given differential equation is - e + 2x2 – 5 yo - y we corresporting to the special form en of RoHS of ☺ , choose trial solution for particular solution and to special form 2x2-5 of Riftes of @ choose friend solution for Yp ( non

Az 't Az x + Ayx2 combining these, we take the most appropriate from for the particular solution Jp ( Yp (u) = A, e A, eu & Azt A & + A42 Where AI, A2, A3, Ay are undetermined constants, Ang