Consider the linear DE$$d$2$ydx$2+$p$($x$)$dydx$+$q$($x$)$y$=$g$($x$)$defined for$$x $$in an interval$$I$.$

Select all that apply.$$

The DE is homogeneous if$$g$($x$)=0$for all x $$on$$I$.$

The DE is homogeneous if$$q$($x$)=0$for all x$$on$$I$.$

The DE is non$-$homogeneous if$$p$($x$)0$for all x$$on$$I$.$

The particular solution$$yp$$of the DE satisfies$$d$2$ydx$2+$p$($x$)$dydx$+$q$($x$)$y$=0.$

The complementary function yc$$of the DE satisfies$$d$2$ydx$2+$p$($x$)$dydx$+$q$($x$)$y$=0.$