Find the most general solution to the non-homogeneous equation.

Question

Find the most general solution to the non-homogeneous equation:

y" - 16y' + 64y = (e^-8x) / (1+x²)

With the given conditions: y(0) = -10 and y'(0) = 9

I partially solved it, with

y = e^8x ∫₀^x ((-te^-16t) / (1+t²))dt + xe^8x ∫₀^x ((e^(-16t)) / (1+t²))dt + ________

I am not sure what the blank part is.

Answer 1

Blank part is general solution o9f homogenius equation: y_GH = (C₁ + C₂x)e^8x