Lotka-Volterra conserved quantity dH/dt ≡ 0 on every trajectory

Exact symbolic verification of conservation. With ẋ = ax - bxy, ẏ = cxy - dy and H(x,y) = cx + by - d ln(x) - a ln(y), direct substitution: dH/dt = (c - d/x)(ax - bxy) + (b - a/y)(cxy - dy). Expanding: (acx - bcxy - ad + bdy) + (bcxy -…