Lecture 2 - Order Degree and Formation of Differential Equations | Ordinary Differential Equations- Order, Degree, Formation - Engineering Mathematics PDF Download

 Page 1


Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper: Ordinary Differential Equations 
Lesson: Order, Degree and Formation of Differential 
Equations 
Lesson Developer: Kapil Kumar 
College/Department: Assistant Professor, Department of 
Mathematics, A.R.S.D. College, University of Delhi 
 
 
 
 
 
 
 
 
 
  
Page 2


Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper: Ordinary Differential Equations 
Lesson: Order, Degree and Formation of Differential 
Equations 
Lesson Developer: Kapil Kumar 
College/Department: Assistant Professor, Department of 
Mathematics, A.R.S.D. College, University of Delhi 
 
 
 
 
 
 
 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.2 
 
Table of Contents 
 Chapter: Order, Degree and Formation of Differential Equations 
? 1: Learning Outcomes 
? 2: Introduction 
? 3: Order Of a Differential Equation 
? 4: Degree Of a Differential Equation 
? 5: Linear and Non-linear Differential Equations 
? 6: Ordinary and Partial Differential Equations 
? 7: Solution of Differential Equations 
o 7.1: General Solution or Complete Primitive 
o 7.2: Particular Solution 
o 7.3: Singular Solution 
? 8: Formation of Differential Equations 
? Exercises 
? Summary 
? Reference 
 
 
  
Page 3


Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper: Ordinary Differential Equations 
Lesson: Order, Degree and Formation of Differential 
Equations 
Lesson Developer: Kapil Kumar 
College/Department: Assistant Professor, Department of 
Mathematics, A.R.S.D. College, University of Delhi 
 
 
 
 
 
 
 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.2 
 
Table of Contents 
 Chapter: Order, Degree and Formation of Differential Equations 
? 1: Learning Outcomes 
? 2: Introduction 
? 3: Order Of a Differential Equation 
? 4: Degree Of a Differential Equation 
? 5: Linear and Non-linear Differential Equations 
? 6: Ordinary and Partial Differential Equations 
? 7: Solution of Differential Equations 
o 7.1: General Solution or Complete Primitive 
o 7.2: Particular Solution 
o 7.3: Singular Solution 
? 8: Formation of Differential Equations 
? Exercises 
? Summary 
? Reference 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.3 
 
1. Learning outcomes: 
After studying this chapter you should be able to understand the 
? Order Of a Differential Equation 
? Degree Of a Differential Equation 
? Linear and Non-linear Differential Equations 
? Ordinary and Partial Differential Equations 
? Solution of Differential Equations 
? General Solution or Complete Primitive 
? Particular Solution 
? Singular Solution 
? Formation of Differential Equations 
 
 
 
 
 
  
Page 4


Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper: Ordinary Differential Equations 
Lesson: Order, Degree and Formation of Differential 
Equations 
Lesson Developer: Kapil Kumar 
College/Department: Assistant Professor, Department of 
Mathematics, A.R.S.D. College, University of Delhi 
 
 
 
 
 
 
 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.2 
 
Table of Contents 
 Chapter: Order, Degree and Formation of Differential Equations 
? 1: Learning Outcomes 
? 2: Introduction 
? 3: Order Of a Differential Equation 
? 4: Degree Of a Differential Equation 
? 5: Linear and Non-linear Differential Equations 
? 6: Ordinary and Partial Differential Equations 
? 7: Solution of Differential Equations 
o 7.1: General Solution or Complete Primitive 
o 7.2: Particular Solution 
o 7.3: Singular Solution 
? 8: Formation of Differential Equations 
? Exercises 
? Summary 
? Reference 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.3 
 
1. Learning outcomes: 
After studying this chapter you should be able to understand the 
? Order Of a Differential Equation 
? Degree Of a Differential Equation 
? Linear and Non-linear Differential Equations 
? Ordinary and Partial Differential Equations 
? Solution of Differential Equations 
? General Solution or Complete Primitive 
? Particular Solution 
? Singular Solution 
? Formation of Differential Equations 
 
 
 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.4 
 
2. Introduction: 
 An Equation involving derivatives or differentials of one or more dependent 
variables with respect to one or more independent variables is called differential 
equations. In this lesson, we will study order and degree of differential equation, three 
types of solutions i.e. general, particular and singular solution and also learn how to 
form differential equations. 
  
Page 5


Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper: Ordinary Differential Equations 
Lesson: Order, Degree and Formation of Differential 
Equations 
Lesson Developer: Kapil Kumar 
College/Department: Assistant Professor, Department of 
Mathematics, A.R.S.D. College, University of Delhi 
 
 
 
 
 
 
 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.2 
 
Table of Contents 
 Chapter: Order, Degree and Formation of Differential Equations 
? 1: Learning Outcomes 
? 2: Introduction 
? 3: Order Of a Differential Equation 
? 4: Degree Of a Differential Equation 
? 5: Linear and Non-linear Differential Equations 
? 6: Ordinary and Partial Differential Equations 
? 7: Solution of Differential Equations 
o 7.1: General Solution or Complete Primitive 
o 7.2: Particular Solution 
o 7.3: Singular Solution 
? 8: Formation of Differential Equations 
? Exercises 
? Summary 
? Reference 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.3 
 
1. Learning outcomes: 
After studying this chapter you should be able to understand the 
? Order Of a Differential Equation 
? Degree Of a Differential Equation 
? Linear and Non-linear Differential Equations 
? Ordinary and Partial Differential Equations 
? Solution of Differential Equations 
? General Solution or Complete Primitive 
? Particular Solution 
? Singular Solution 
? Formation of Differential Equations 
 
 
 
 
 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.4 
 
2. Introduction: 
 An Equation involving derivatives or differentials of one or more dependent 
variables with respect to one or more independent variables is called differential 
equations. In this lesson, we will study order and degree of differential equation, three 
types of solutions i.e. general, particular and singular solution and also learn how to 
form differential equations. 
  
Order, Degree and Formation Of Differential Equations 
       
Institute of Lifelong Learning, University of Delhi                                                 pg.5 
 
3. Order of a Differential Equation: 
     The order of the highest order derivative involved in a differential equation is called 
the order of the differential equation.  
Example 1: 
Find the order of the following differential equations.
  
 (i)   
3
2
2
dy
dx
??
??
??
 + x
5
dy
dx
??
??
??
  + y=
2
x  
 (ii)
y=
x
 
dy
dx
??
??
??
 + k/(
/ dy dx
 ) 
Solution: (i) It is of the second order because the order of the highest derivative is 2. 
(ii) It is of the first order because the order of the highest derivative is 1.