i) IF $\frac{dy}{dt} = - \frac{∂H}{∂z}, \frac{dz}{dt}= \frac{∂H}{∂y}$

where H is a function of $y$ and $z$, show that $H(y,z)$ is constant in time.

ii) Take a $H(y,z) =Ay^2 + 2Hyz + Bz^2$ where $A,B,H$ are constants and show that solutions of the system lie on ellipses.

iii) Apply the explicit Euler and the symplectic Euler schemes to the system in (ii) and check whether the area is preserved.

can anyone tell me how to start. totally confused.