y(0)=9 and y'(0)=2
none in particular
The Attempt at a Solution
First I solved for the auxiliary equation.
So the general solution for the homogenous form is C1e0x+C2e4x where C1 and C2 are unknown coefficients to be found.
The particular solution is calculating by considering Yp= AXe4x
Differentiating that twice, and solving for Yp, I get Yp=15xe4x
So the general solution for this is obtained by adding the homogeneous and the particular. So I get: C1e0x+C2e4x +15xe4x
I differentiated this equation and got 4C2+15e4x+60x4x
So then I got 4C2+15=2, so C2=-3.25
Also, from the general solution C1+C2=9, so C1=12.25
The final answer I got was (12.25)e0x+-3.25e4x+15xe4x but this is wrong. Any ideas?