Consider the following ODE

Urcos$+\frac{M}{2}+(Usin)\frac{dr}{d}=0$

a$)$ Show that this expression is exact.

b$)$ Find the general solution to this expression.

c$)$ Plot multiple solutions to this equation with $M=1$ and $U=1.$ Use the matplot lib.pyplot.contour command to plot.

d$)$ Add a bold red line to the plot for where $(r,)=\frac{M}{2}.$ You can use the formulas $x=r**cos()$ and $y=r**sin()$ to convert from $(r,)$ to $(x,y).$ This streamline represents the surface of a Rankine half$-$body and it is used in modeling flow around solid bodies.