Order and degree of a differential equation
(For IIT-JEE Preparation)
IITians at your home
ISO 9001:2008 Certified
India's No. 1 Online Academy
Contact: +91-9555288846
operations_kei
09718199348
Order and degree of a differential equation

Order of a differential equation
order of a differential equation is defined as the order of the highest order derivative of the dependent variable with respect to the independent variable involved in the given differential equation.
Consider the following differential equations:
order of a differential equation The equations (6), (7) and (8) involve the highest derivative of first, second and third order respectively. Therefore, the order of these equations are 1, 2 and 3 respectively.

Degree of a differential equation
To study the degree of a differential equation, the key point is that the differential equation must be a polynomial equation in derivatives, i.e., y′, y″, y″′ etc. Consider the following differential equations:
degree of a differential equation We observe that equation (9) is a polynomial equation in y″′, y″ and y′, equation (10) is a polynomial equation in y′ (not a polynomial in y though). Degree of such differential equations can be defined. But equation (11) is not a polynomial equation in y′ and degree of such a differential equation can not be defined.

By the degree of a differential equation, when it is a polynomial equation in derivatives, we mean the highest power (positive integral index) of the highest order derivative involved in the given differential equation.

In view of the above definition, one may observe that differential equations (6), (7), (8) and (9) each are of degree one, equation (10) is of degree two while the degree of differential equation (11) is not defined.

NOTE: Order and degree (if defined) of a differential equation are always positive integers.

Example Find the order and degree, if defined, of each of the following differential equations:
order and degree of a differential equation

Solution
(i) The highest order derivative present in the differential equation is order of a differential equation, so its order is one. It is a polynomial equation in y′ and the highest power raised to order of a differential equation is one, so its degree is one.
(ii) The highest order derivative present in the given differential equation is order and degree of a differential equation, so its order is two. It is a polynomial equation in order and degree of a differential equation and order and degree of a differential equation and the highest power raised to order and degree of a differential equation is one, so its degree is one.

(iii) The highest order derivative present in the differential equation is y′′′ , so its order is three. The given differential equation is not a polynomial equation in its derivatives and so its degree is not defined.

Do you like this Topic?
Share it on
      
      

IIT JEE Maths Study Material

Skip Navigation Links.
Collapse MathsMaths
Collapse AlgebraAlgebra
Expand SetsSets
Expand Sequences and seriesSequences and series
Expand Complex NumbersComplex Numbers
Expand Quadratic EquationsQuadratic Equations
Expand Linear inequalitiesLinear inequalities
Expand Permutations and CombinationsPermutations and Combinations
Expand ProbabilityProbability
Expand Binomial theoremBinomial theorem
Expand Matrices and determinantsMatrices and determinants
Collapse TrignometryTrignometry
Collapse CalculusCalculus
Expand Relations and FunctionsRelations and Functions
Expand Limits and DerivativesLimits and Derivatives
Expand Continuity and DifferentiabilityContinuity and Differentiability
Expand Applications of derivativesApplications of derivatives
Expand Integral calculusIntegral calculus
Expand Application of integralsApplication of integrals
Expand Differential equationsDifferential equations
Collapse Coordinate GeometryCoordinate Geometry
Vector and 3D Geometry

Free IIT JEE Study Material

  • Online Classroom Program

    • IITians @ Your Home, Attend Classes directly from Home
    • Two way interaction between Teacher and Students
    • Zero Travel Time or Cost involved, No Hidden Charges
    • Small Batch Sizes, Maximum of 12-15 Students
    • Golden Opportunity to be trained by IITians and NITians
    • All you need is a Computer / Laptop & Internet Connection
    Try Free Demo Class IIT JEE Online Classes
  • 1 on 1 Online Class

    • IITians @ your Home for 1 on 1 Class
    • Two way Communication between Teacher and Student
    • Special Doubt Removal & Problem solving Sessions
    • Customize the Course as per your desire - Duration, Timing, Faculty etc
    • All faculties are IITians and NITians
    • All you need is a Computer / Laptop & Internet Connection
    Try Free Demo Class IIT JEE 1 on 1 Online Classes
  • Correspondence Course Details

    • 600 Hours of Recorded Lectures by IITians and NITians
    • Best Study Material comprising all Concepts and Tricks
    • 10000+ Solved Question Bank + 250 Hours of Video Solutions
    • Complete NCERT solutions + 150 Hours of NCERT Video Solutions
    • Last 30 years JEE chapterwise video solutions
    • 100% Original Material prepared by JEE Experts
    Register for Free Now IIT JEE Correspondence Courses
  • AITS for JEE Main and JEE Advanced

    Register for Free Now JEE Test Series
[X]
Welcome to Kshitij Education India

Kshitij Education India as an organisation is immensely grateful to society at large and has made efforts to contribute to the Indian Education system. The free study material section of our website can be deemed as a treasure of resources sufficient for an aspirant to clear JEE Mains. Kshitij provides past year solutions of IIT, AIEEE, JEE Mains and Advanced in its free study material section. Our faculty members put in best efforts to explain each and every question in the best possible manner. Online IIT JEE Free Study Material section also features a collection of over 10,000 pages of study resources covering the entire IIT JEE curriculum. Our discussion forum stimulates a student intellectually with over 5000 threads of IIT discussion topics.

Please enter the Email Id and Contact number of the person to whom you would like to refer www.kshitij-iitjee.com




[X]
Welcome to Kshitij Education India
Our Guarantee:
  1. We're so sure you'll have the time of your life with us, we back our courses with a 100% Satisfaction Guarantee.
  2. If for any reason you aren't 100% satisfied with your classes in first 7 days, just let us know and we'll refund your fees. No questions asked.*
  3. And based on your feedback, we will take the necessary steps to ensure we never repeat any mistakes as such.

* It is mandatory to attend first 7 days of live classes and than if you found any valid reason to step back you can request us for refund.

Live Chat