$(a)(10pts)$ For the ODEs below indicate their order and whether they are linear

$or$ nonlinear. $In$ the case that they are nonlinear indicate the responsible

term.

$i.u\frac{du}{dt}+t^2=3u,$ where $uis$ a function $oft.$

$ii.x^{\text{'}\text{'}}+t^2{x}^{\text{'}}x+t=0,$ where $xis$ a function $oft.$

iii. $\frac{dx}{dt}=xcot(t)log(t),$ where $xis$ a function $oft.$

$(b)(10pts)$ Solve the ODE below. What $is\underset{t}{lim}y(t)?$

$\frac{dy}{dt}=\frac{9t^2}{(t^3+8{)}^2},y(0)=1$