5. \{y_1(x) = x, y_2(x) = x \ln x\} is a fundamental set of solutions of the reduced equation of
$y'' + p(x)y' + q(x)y = \frac{2}{x}$
Find the equation and find a particular solution.
(a) $y'' - \frac{2}{x}y' - \frac{2}{x^2}y = \frac{2}{x}$, $z = 2x(\ln x)$
(b) $y'' - \frac{1}{x^2}y = \frac{2}{x}$, $z = x^2 \ln x$
(c) $y'' - \frac{1}{x}y' + \frac{1}{x^2}y = \frac{2}{x}$, $z = x(\ln x)^2$
(d) $y'' - \frac{1}{x}y' - \frac{1}{x^2}y = \frac{2}{x}$, $z = x^2 \ln x - x(\ln x)^2$
(e) None of the above.