Word Count : 134

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((D^3+2D^2-D-2)y=e^x+x^2) means [ y''' +2y''-y'-2y=e^x+x^2. ] First find the complementary function by solving the auxiliary equation [ m^3+2m^2-m-2=0. ] Grouping, [ (m^3+2m^2)-(m+2)=m^2(m+2)-1(m+2)=(m+2)(m^2-1)=0. ] Hence (m=-2,1,-1). So [ y_c=C_1e^{-2x}+C_2e^{x}+C_3e^{-x}. ] Now find the particular _____ _____ __________ ____ _________ __________.
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