What went wrong with my calculations for a 2nd order D.E. solution?

[asdf1]

for the following question:
y``+y`+9.25y=2+2x+x^2

my problem:
yh=c1+c2e^(-x)
suppose yp=c3x^2 + c4x+c5
then yp`=2c3x+c4
so yp``=2c3

then 2c3+2c3x+c4=2+2X+X^2
so c3=1, c4=1
so yp=x^2+x
then y=c1+c2e^(-x)+x^2+x
which implies c1=8
=> y=8+c2e^(-x)+x^2+x
so y`=-c2e^(-x)+2x+1
so -1=-c2+1 =>c2=2
then y=8+2e^(-x)+x^2 +x

but the correct answer should be 3e^(-x)+5+2x+(1/3)x^3
does anybody know what's wrong with the calculations?

 

[homology]

for the following question:
y``+y`+9.25y=2+2x+x^2
my problem:
yh=c1+c2e^(-x)

According to what you have written your homogeneous solution isn't a homogeneous solution:

(c_2e^(-x))+(-c_2e^(-x))+9.25(c_1+c_2e^(-x))=9.25(c_1+c_2e^(-x)) which isn't zero (unless both constants are zero)

 

[asdf1]

jeepers! i'll recheck that again! thanks!