We know that $y_1(x)=x^{2}$ is a solution to the differential equation $x^2 D^2y + 7 x D y - 16 y=0$ for $x \in (0,\infty)$. Use the method of reduction of order to find a second solution to $x^2 D^2y + 7 x D y - 16 y=0$ for $x \in (0,\infty)$.

(a) After you reduce the second order equation by making the substitution $w = u'$, you get a first order equation of the form
$w' = f(x,w) =$ .
Note: Make sure you use a lower case w, (and don't use w(t), it confuses the computer).

(b) A second solution to $x^2 D^2y + 7 x D y - 16 y=0$ for $x \in (0,\infty)$ is
$y_2(x) =$ .