This is an example of A DE with Homogeneous Coefficients

ie it can be written in the form dy/dt = f(y/t)

dy/dt = 1/3 t/y + 1/3 y/t

Let z= y/t

tz = y

and z + tdz/dt = dy/dt

z + t dz/dt = 1/(3z) + 1/3z

tdz/dt = 1/(3z) - 2z/3

you now have a separable equation I'll let you go from here