The aux. equation
p^2-3p+2 =0
(p-1)(p-2)=0
p=1 or 2
let
yp = (A+Bx+Cx^2)e^x
yp' = [(A+B)+(B+2C)x+ Cx^2].e^x
yp''= [(A+2B+2C)+(B+4C)x+ Cx^2].e^x
yp''-3yp'+2yp = xe^x
[(A+2B+2C)+(B+4C)x+ Cx^2].e^x -3 [(A+B)+(B+2C)x+ Cx^2].e^x
+2(A+Bx+Cx^2)e^x =xe^x
[(-B+2C)-2Cx]e^x =xe^x
C = -1/2
-B+2C =0
-B -1 =0
B=-1
yp = [A -x - (1/2)x^2].e^x
y= De^(2x) +[A -x - (1/2)x^2].e^x
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