Given $\displaystyle {y}_{{1}}{\left({x}\right)}={x}^{{4}}$ satisfies the corresponding homogeneous equation of

$\displaystyle {x}^{{2}}{y}{''}-{x}{y}'-{8}{y}=-{18}{x}+{24},\quad{x}>{0}$

Then the general solution to the non-homogeneous equation can be written in the form $\displaystyle {y}{\left({x}\right)}={A}{x}^{{4}}+{B}{x}^{{n}}+{y}_{{p}}$.

Use reduction of order to find the general solution in this form (your answer will involve A, B, and x)

$\displaystyle {y}{\left({x}\right)}$ = Preview Question 6