Gradescope problem $\backslash$#$11$: As part of your work Classify the differential equation by order and linearity and tell me the name of the method you will use to solve the problem Find the general solution of the given differential equation.

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

x $\backslash$frac$\{$d y$\}\{$d x$\}+3$ y$=$x$^\{3\}-$x $\backslash \backslash$

y$($x$)=$

$\backslash$end$\{$array$\}$

$\backslash ]$

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.$)$