can you please help me find the Particular Solution for these problems:

The general solution: y = yc +yp where, yc = complimentary solution Jp = particular solution Methods in determining Particular Solution (Vp) (1) Reduction of Order (2) Variation of Parameter (3) Undetermined Coefficient\f\f4 . (0 2 - 5 D + 6 ) y = 20* +12 using variation of Parameters - For YC : M 2 - 5m+ 6 = 0 ( m- 2) ( m - 3 ) = 0 mi = 2 , m2 = 3 The complimentary solution is yc= cies* + cze3x -+ For Up: Replace c, and c2 by pond Q ( where Pand Q are parameters to be determined ) y = pe ?*+ Qe 3X 1 Differentiate, yl = p2e 2x + ple 2X+ Q3e3x+ @ @3X setting plex + Qle 37 = 0 (2) y' = Pze 27 + Qge3X (3) Differentiate, y" = 4 pe 2 X + 2 ple 2X + 90e37 + 3 Q'23X (4) substitute @, 3 and 4) in the given equation and simplify, 2 ple 27 + 3 Q'e 3x = 20* + 12 ple z x = ex + 6 - 3 Q' e 3 X 5 2 substitute (5) in ( 2 ) Q' = 20- 27 + 120- 3X integrate, - Q = - e - 2X_4 0-3X subst (6) in (2), P' = 20- - 120 - 2X integrate, -P = 2 0- 120- 2X substitute Pand Q in (1 The Particular solution is, yp = ex + 2