请问怎么求streakline和trajectory的方程啊？

xiaosanshao

各位大虾，请问怎么求streakline和trajectory的方程啊？比如下面这道题
Given is a planar velocity field (2D), in which the velocity component in x-direction is described as u=kx .
a) Calculate the stream function of the given flow field.
b) Determine the equation for the velocity component in y-direction v.
Now assume the strength k of velocity filed to be time dependent:
k=a+b*sinwt given that the constant a > b > 0.
c) Sketch the amplitude of the velocity for a fixed position P(x0, y0)
qualitatively.
d) Compute the equation of the streamline through the point P(x0, y0).
e) Compute the equation of the trajectory (path line)through the point P(x0, y0).
f) Calculate the streakline through the origin.