$In$ Problems $14-24$ find the general solution $of$ the given differential

equation. Give the largest interval I over which the

general solution $is$ defined. Determine whether there are any

transient terms $in$ the general solution.

$14.$

$x{y}^{\text{'}}+(1+x)y=e^{-x}sin2x$

$15.$

$ydx-4(x+y^6)dy=0$

$16.$

$ydx=(y{e}^y-2x)dy1$

$17.$

$cosx\frac{dy}{dx}+(sinx)y=1$

$18.$

$co{s}^{2}xsinx\frac{dy}{dx}+(co{s}^{3}x)y=1$

$19.$

$(x+1)\frac{dy}{dx}+(x+2)y=2x{e}^{-x}$

$20.$

$(x+2{)}^2\frac{dy}{dx}=5-8y-4xy$

$21.$

$\frac{dr}{d}+rsec=cos$

$22.$

$\frac{dP}{dt}+2tP=P+4t-2$

$23.$

$x\frac{dy}{dx}+(3x+1)y=e^{-3x}$