$(50$ points$)$ Consider a velocity field with

$u=y+e^{-3t}$

$v=3t^2$

$($a$)$ Find the streamline that passes through the point $(1,1)$ at different times.

$($b$)$ Determine the path line of a particle that was at $(1,1)$ at time $t=0.$

$($c$)$ Find the streak line of point $(1,1)$ at time $1.$

$($d$)$ Evaluate the deformation rate tensor.