How to find constants of motion from this hamiltonian?

[Flamboyanza]

Given H=p^2/2 - 1/(2q^2)
How to show that there is a constant of motion for this one dimensional system D=pq/2 - Ht ?

I tried doing it in my usual way i.e. p'=-∂H/∂q and q'=∂H/∂p and then finding the constants of motion but that doesn't match with what I have to show.

Please guide me as to how to proceed?

 

[Hypersphere]

You can definitely use Hamilton's equations to show that D is a constant of motion. Are you sure you did calculate $\dot{D}=\frac{d D}{dt}$ correctly?

 

[vela]

You need to show your work so we can see where the problem might lie.