Find the general solution of the given differential equation.

y$=2$y $+$ x$2+7$

y$($x$)=$

$$Ce$2$x$$x$22$x$2154$

Good work.

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

$$$($$,$$)$

Great!

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.$)$

$$NONE

Good!