$(1$ point$)$ Given the Cauchy$-$Euler equation,

x$2$y$+5$xy$4$y$=0,$x$2$y$+5$xy$4$y$=0,$

find the roots of the auxiliary equation $($listed in increasing order, if applicable$)$

and

and the solution given that the constants of integration are equal to one.

y$=$y$=$