Evaluating first order differential equation

Question

I was given $$(x+3y^2)\frac{dy}{dx}=y$$ and also $y>0$ so I wrote it as $$\frac{dx}{dy}=\frac{x}{y} + 3y$$ now substituting $x=y.t$ and $$ \frac{dx}{dy}=t+y.\frac{dt}{dy}$$ I am finally left with $$dt=3dy$$ Integrating which becomes $$t=3y+c_1=x/y$$ Is this correct??