Given $\displaystyle {y}_{{1}}=\frac{{1}}{{{x}-{1}}}$ and $\displaystyle {y}_{{2}}=\frac{{1}}{{{x}+{1}}}$ satisfy the corresponding homogeneous equation of

$\displaystyle {\left({x}^{{2}}-{1}\right)}{y}{''}+{4}{x}{y}'+{2}{y}=\frac{{1}}{{{x}+{1}}}$

Use variation of parameters to find a particular solution $\displaystyle {y}_{{p}}={u}_{{1}}{y}_{{1}}+{u}_{{2}}{y}_{{2}}$

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