Chapter 3.6, Problem 1P

For each of the systems in Problem $1$ through $6$:

a) Find an equation of the form $H\left(x,y\right)=C$ satisfied by the solution of the given system.

b) Without using a computer, sketch some level curves of the function $H\left(x,y\right)$.

c) For $t>0$, sketch the trajectory to corresponding to the given initial condition and indicate the direction of the motion for increasing $t$.

$\frac{dx}{dt}=-x,\frac{dy}{dt}=-2yx\left(0\right)=4y\left(0\right)=2$