Lesson 2 of 9 · 5 min
Order of a differential equation
NCERT §9.2.1
One entry in the log compares acceleration and speed. Before solving anything, the club labels each equation by how many times y has been differentiated.
The lesson in notes
In short
The order is the order of the highest derivative of the dependent variable that appears in the equation.
dy/dx = cos x has order 1. y″ + 4y = 0 has order 2. (y‴)² + x y′ = 0 has order 3.
Powers do not change the order: (y″)³ + (y′)⁵ + y = 0 still has order 2, because y″ is the highest derivative present.
Order is always a positive integer, and it can always be read off, whatever else the equation contains.
The order also tells how many arbitrary constants a general solution carries: an equation of order n has a general solution with n independent constants.