We know that $y_1(x)=e^{19 x}$ is a solution to the differential equation $D^2y - 38 D y + 361 y=0$ for $x \in (-\infty,\infty)$. Use the method of reduction of order to find a second solution to $D^2y - 38 D y + 361 y=0$ for $x \in (-\infty,\infty)$.

(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 $D^2y - 38 D y + 361 y=0$ for $x \in (-\infty,\infty)$ is
$y_2(x) =$

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