Find the streamlines of the velocity field

Question

I have to find the streamlines of the following velocity fields:

1. $$u=x(1+2t), v=y$$
2. $$u=xy, v=0$$

I have done the following:

1. $$\frac{dx}{u}=\frac{dy}{v} \Rightarrow \frac{dx}{x(1+2t)}=\frac{dy}{y} \Rightarrow \frac{\ln x}{1+2t}=\ln y+c \Rightarrow y=Ce^{\frac{\ln x}{1+2t}} \Rightarrow y=Cx^{\frac{1}{1+2t}}$$

   Is this correct??

2. $$\frac{dx}{u}=\frac{dy}{v} \Rightarrow \frac{dx}{xy}=\frac{dy}{0}$$

   How could we continue??