Problem $3$: $(3$ points, $1$ point each$)$ Solve using separation $of$ vars

$(a)(Implicit$ form$)$

$\frac{dy}{dt}=\frac{tsec(y)}{y(e^{t^2})}$

$(b)(Remember$ the initial condition$)$

$\frac{dy}{dt}=\frac{2t+se{c}^2(t)}{2y}$

$y(0)=-5$

$(c)(Bewareof$ hidden solutions, see last example $in$ the notes$)$

$\frac{dy}{dt}=\frac{-t(y-1{)}^2}{3}$