Which of the following is the appropriate form for a particular solution of the differential equation y (4) + 3y 00 − 4y = 2x + cos2 x − cosh x ? (a) yp = (A + Bx)e x + (C + Dx) cos(2x) + (E + F x) sin(2x) (b) yp = (Ax + B)e −x + (C + Dx) cos(−x) + (E + F x) sin(−x) (c) yp = Ax + Bx2 + (C + Dx) cos x + (E + F x) sin(−x) + Ge2x (d) yp = Ax + Bx2 + (C + Dx) cos(2x) + (E + F x) sin(−2x) + Ge−x (e) yp = A + Bx + Cx sin(−2x) + Dx cos(2x) + Exex + F xe−x
Correesponding homogeneous differential equation
Characteristic (auxiliary) equation
The general solution of the homogeneous differential equation is
Then the appropriate form for a particular solution of the given non homogeneous differential equation is
(e)
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