= Solution
Integrating $\psi_y=x+\sin t$ and imposing $-\psi_x=-y$ gives the <streamfunction>
$$
\boxed{\psi(x,y,t)=y(x+\sin t)}
$$
up to an arbitrary function of time. At the specified time, the <streamlines> are
$$
\boxed{y(x+1)=C}.
$$
For $C\ne0$, the connected branches are rectangular hyperbolas. The zero level consists of the lines $y=0$ and $x=-1$, with the <stagnation point> $(-1,0)$ at their intersection; their half-lines and the stationary point are the distinct <streamlines>.
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