Chapter 3.6, Problem 6P

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 solutions 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 $t$.

$\frac{dx}{dt}=2y,\frac{dy}{dt}=-8xx\left(0\right)=1y\left(0\right)=2$