Answer
$$y\left( t \right) = C{t^{ - 3}}{\text{ is a solution of the given differential equation}}$$
Work Step by Step
$$\eqalign{
& y\left( t \right) = C{t^{ - 3}} \cr
& {\text{differentiate}} \cr
& y'\left( t \right) = C\left( { - 3{t^{ - 2}}} \right) \cr
& y'\left( t \right) = - 3C{t^{ - 2}} \cr
& {\text{replace }}y\left( t \right){\text{ and }}y'\left( t \right){\text{ in the differential equation }} \cr
& ty'\left( t \right) + 3y = 0 \cr
& t\left( { - 3C{t^{ - 2}}} \right) + 3C{t^{ - 3}} = 0 \cr
& {\text{simplify}} \cr
& - 3tC{t^{ - 2}} + 3C{t^{ - 3}} = 0 \cr
& 0 = 0 \cr
& {\text{then}} \cr
& y\left( t \right) = C{t^{ - 3}}{\text{ is a solution of the given differential equation}} \cr} $$
