Find the general solution $of$ the given differential equation.

$y(x)=$obrace$({)}^{x^2{y}^{\text{'}}+xy}=5$

Give the largest interval over which the general solution $is$ defined. $(Think$ about the implications $of$ any singular points. Enter your answer using interval notation.$)$

Determine whether there are any transient terms $in$ the general solution. $(Enter$ the transient terms $as$ a comma$-$separated list; $if$ there are none, enter NONE.$)$