Third Order Non-Homogenous ODE

Iam having trouble in finding the particular solution for this DE, thas really the most hardest thing to me always but this is what i did the DE itself is;

If found my homogenous side which turned out to be; ( am using method of undetermined coefficients we have learned all the other easy ways thier is to do this i guess)

(homogeneous side), for my particular guess ;

since bx appeard in this homogenous and the constant c also appears i multiplied them by x so my final guess was

when i equate terms and solve i get a=2 b=0 c=0? am not sure were my mistake is or if my intial guess itself is incorrect! thanks!! in advance