Create a function, mystreamline $(u,v,x,y)$ to compute the streamlines for a given velocity field

$u(x,y)$ and $v(x,y).$ Assume the following: $(30$ marks$)$

Groups I and II

$u(x,y)=c\frac{x}{x^2+y^2}$

$v(x,y)=c\frac{y}{x^2+y^2}$

Groups III and IV

$u(x,y)=c\frac{y}{x^2+y^2}$

$v(x,y)=-c\frac{x}{x^2+y^2}$

Groups V$,$ VI and VII

$u(x,y)=cx$

$v(x,y)=-cy$

where c is a constant. Compute the streamlines analytically. Thereafter compute the

streamlines numerically and compare them with the analytical solution in a domain $[x,y]sube$

$\left[\begin{array}{cc}-1& 1\\ -1& 1\end{array}\right].$ Use the inbuilt matlab function to compare the streamlines. Now, compute

the pathlines numerically using a similar method mypathline$(u,v,x,y,t$ for $20$ particles starting

from random locations on the domain and show that they lie on the streamlines. Identify the

stagnation points if any. please answer every part