Put the differential equation $\displaystyle \frac{t y^{\,\prime}}{(t^{2}+3) y} = \cos(t) + \frac{e^{4 t}}{y}$ into the form $y^{\,\prime} + p(t) y = g(t)$ and find $p(t)$ and $g(t)$.

$p(t) =$ help (formulas)
$g(t) =$ help (formulas)

Is the differential equation $\displaystyle \frac{t y^{\,\prime}}{(t^{2}+3) y} = \cos(t) + \frac{e^{4 t}}{y}$ linear and homogeneous, linear and nonhomogeneous, or nonlinear?

Answer: Choose linear and homogeneous linear and nonhomogeneous nonlinear