Consider the differential equation

$\frac{dy}{dt}=q_1(t)+q_2(t)y+q_3(t)y^2$

where $q_1,q_2,q_3$ are functions. Suppose that some particular solution $y_{1}of$ this equation

$is$ known. Another family $of$ solutions can $be$ obtained through the substitution

$y(t)=y_1(t)+\frac{1}{v(t)}$

$av$ satisfies the simpler equation

$\frac{dv}{dt}=-(q_2+2q_3{y}_1)v-q_3$

$b\frac{dy}{dt}=\frac{-2co{s}^{2}t-si{n}^{2}t+y^2}{2cost}$

Find a solution $to$ this equation.

Hint $1$: $It$ doesn't need $tobe$ the most general solution! Any one will

$do.$

Hint $2$: Look for a function which $is$ bounded, and where the derivative

$is$ bounded for all $R.$ What choices $ofy$ might keep the ODE's right$-$hand

side finite?

$c$