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Solve (D2-3D+2)y =x(x+4) and show that its general solution is given by y=Aex + Be2x +(x2/2) + (7x/2) + (19/4)
My work :
auxiliary eqn , m2 - 3m + 2= 0 m=1 , m=2
Reduced eqn : yn = Aex + Be2x
P.I. = 1/f(D)F(x) = (1/(D2-3D+2))(x(x+4))
P.I. = [(x2+4x) + ( (1/2)( 2- 3(2x) - 3(4) ) ) + (1/4)(92) )
P.I. = x2 + (4x/2) - (6x/4) - (5/2) + (18/4)
P.I. =(x2/2) + x + 8/4
General solution : y= Aex + Be2x + (x2/2) + x + 8/4
Could anyone point out my mistakes?