What is the difference between an Ordinary Demand equation and an Engel curve equation? I mean, an Ordinary Demand Equation measures changes in quantity of X due to changes in price Px.  Engel Curve measures changes in quantity of X due to changes in income M.  But ODE has M in it's equation, and is simply just an algebraic variant of the Engel curve!
Engel curve assumes the price is constant, and demand curve assumes income constant. There is only demand function, no engel curve equation or demand equation.