For the differential equation

$\displaystyle {y}{''}-{10}{y}'+{34}{y}=-{68}{x}^{{2}}+{380}{x}+{236}+{161}{e}^{{x}}+{200}{x}{e}^{{x}}$

Find the solution of the associated homogeneous equation. Use $\displaystyle {c}_{{1}}$ and $\displaystyle {c}_{{2}}$ as constants, and use $\displaystyle {c}_{{1}}$ for the cosine term and $\displaystyle {c}_{{2}}$ for the sine term.

$\displaystyle {y}_{{c}}=$ Preview Question 6 Part 1 of 2  

Use the method of undetermined coefficients to find the particular solution.

$\displaystyle {y}_{{p}}=$ Preview Question 6 Part 2 of 2