Here is the problem:

y

−12y

+32y

=21ex

y(0)=27

y

(0)=21

y

(0)=25

Y(x) = ??

I used the method of undetermined coefficients and my answer is:

(71/3)+(8/3)e^(4x)+(-1/3)e^(8x)+e^x

But the online-homework wouldn't accept it and says it's incorrect...

Here is what I did:

Yp(x) = (C1) + (C2)e^(4x) + (C3)e^(8x) + e^x

Y'p(x) = 4(C2)e^(4x) + 8(C3)e^(8x) + e^x

Y''p(x) =

**8**(C2)e^(4x)+64(C3)e^(8x) + e^x

(that 8 should be 16)
then after plug in and used the given initial values I got:

(C1) + (C2) + (C3) + 1 = 27

4(C2) + 8(C3) + 1 = 21

**8**(C2) + 64(C3) + 1 = 25

(again, the 8 should be 16)
so C1 = 71/3

C2 = 8/3

C3 = -1/3

(the coefficients in the complementary solution should be different now.)
Please help!!!

Thank You!!