In this problem,

y $=$

$1$x$2+$ c

is a one$-$parameter family of solutions of the first$-$order DE

y$+2$xy$2=0.$

Find a solution of the first$-$order IVP consisting of this differential equation and the given initial condition.

y$(3)=$

$18$

y $=$

Give the largest interval I over which the solution is defined for the given initial condition. $($Enter your answer using interval notation.$)$