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**dif. eq. problem -- dont know why it is wrong**

I did this problem three times with the same wrong answer...

solve for y:

[tex]y'''-9y''+18y'=0[/tex]

y(0)=5

y'(0)=7

y''(0)=6

so I change it into the auxiliary equation then solve for the variables, i get the roots: 3 and 6. so the general solution would be:

[tex]y'=c_1e^{3x}+c_2e^{6x}[/tex]

solving for c1 and c2 i get:

[tex]7=c_1+c_2[/tex]

[tex]2=c_1+2c_2[/tex]

[tex]c_1=12[/tex]

[tex]c_2=-5[/tex]

[tex]y=\int{12e^{3x}-5e^{6x}}[/tex]

[tex]y=36e^{3x}-30e^{6x}+c[/tex]

solving for c when x=0 and y=5, i get

[tex]y=36e^{3x}-30e^{6x}-1[/tex]

what am i donig wrong?