Order, Degree and Formation of Differential Equations
The order of a differential equation is the highest derivative present and the ° is the power of that derivative once the equation is polynomial in derivatives.
What is Order, Degree and Formation of Differential Equations?
The order of a differential equation is the highest derivative present and the ° is the power of that derivative once the equation is polynomial in derivatives.
Key formula / rule: Degree is defined only when the equation is polynomial in its derivatives.
Key points
- Identify the order and ° of a differential equation.
- Derive the differential equation of a family of curves.
Common exam trap
Reading the ° from an equation still containing a radical in a derivative.
Definitions
- Term
Order, Degree and Formation of Differential Equations
- Meaning
The order of a differential equation is the highest derivative present and the ° is the power of that derivative once the equation is polynomial in derivatives.
- Term
Order, Degree and Formation of Differential Equations — explanation
- Meaning
A family of curves with n arbitrary constants gives an equation of order n after eliminating them. Recognising this reverses the usual solving direction and is a standard question type.
Learning objectives
Identify the order and ° of a differential equation.
Derive the differential equation of a family of curves.
Formulae
- Key point
Degree is defined only when the equation is polynomial in its derivatives.
- Key point
Eliminating n arbitrary constants yields an equation of order n.
- Key point
Radicals and fractional powers of derivatives must be cleared before reading the °.
Common mistakes
Reading the ° from an equation still containing a radical in a derivative.
Confusing the highest power of the dependent variable with the °.
Keywords
Order
Degree
Formation
Differential
Practice preview
What is the degree of the differential equation (d2y/dx2)^3 + (dy/dx)^2 + y = 0?…
easy
Find the order and degree of the differential equation (dy/dx)^2 + (dy/dx) - sin^2(y) = 0.…
easy
Determine the degree of the differential equation (d2y/dx2) = (1 + (dy/dx)^2)^(3/2).…
medium