Given a family of curves with n arbitrary constants, the corresponding DE has order n. Process: differentiate the equation n times (generating n+1 equations including the original), then eliminate all n constants algebraically. Example 1: y = $Ae^x$ (1 constant). Differentiate: y' = $Ae^x$ = y. DE: y' = y, order 1. Example 2: y = Acos(x) + Bsin(x) (2 constants). y' = -Asin(x) + Bcos(x). y'' = -Acos(x) - Bsin(x) = -y. DE: y'' + y = 0, order 2. Common JEE problem: "Form the DE for all circles in the xy-plane" — 3 constants (h, k, r), so order 3. For "circles passing through origin touching x-axis": only 1 constant, order 1.