You are given that y=x^12 is a solution of the homogeneous differential equation
x^2\frac{d^2y}{dx^2}-9x\frac{dy}{dx}-24y=0 \text{.}
Now use the method of variation of parameters by setting y=x^{12}v(x), for an unknown function v(x) to be determined, and find the complete general solution of
x^2\frac{d^2y}{dx^2}-9x\frac{dy}{dx}-24y=-6x^{-8} \text{,}
in the form y=Ax^{12}+Bx^β+y_{PI}(x), where A and B are arbitrary constants and y_{PI}(x) is a particular integral.
y=\input