Author : Ravendra Kumar . As Per B.Sc. / B.A. Mathematics Generic Elective syllabus of 2nd Semester (Dibrugarh) & 3rd Semester (Gauhati) under various Indian Universities

Content in Details

**1. Differential Equation of First Order and First Degree 08 – 69**

1.1. Introduction 08-09

1.2. Ordinary and partial differential equation 09-09

1.3. Order of the differential equation 09-09

1.4. Degree of the differential equation 09-09

1.5. Formation of a differential equation 09-14

1.6. Solution of differential equation of first order and first degree 14-15

1.7. Method of separation variable 15-20

1.8. Homogeneous differential equation 20-26

1.9. Equation reducible to homogeneous form 26-34

1.10. Linear differential equation 34-42

1.11. Bernoulli’s equation 42-48

1.12.Exact differential equation 48-54

1.13. Integrating factor 54-57

1.14. Rule for finding integrating factor 57-66

1.15. Change of Variable .66-69

**2. Differential Equation of First Order and Higher Degree 70 – 86**

2.1. Equation solvable for P 70-75

2.2. Equation solvable for Y 75-76

2.3. Equation solvable for X 76-83

2.4. Clairaut equation 83-86

**3. The Wronskian 87 – 106**

3.1. Definition 87-883.2. Linear combination of the function 88-88

3.3. Linear dependent set of function 88-88

3.4. Linear independent set of function 88-88

3.5. Application 88-106

**4. Solution of Differential Equation by Reducing it’s Order 107 – 138**

4.1. Complete solution of second order in term of known integral 107-120

4.2. Removal of first derivative (Transformation to the normal form) 120-129

4.3. Change of independent variable 129-138

**5. Method of Variation of Parameter 139 – 153**

**6. Linear Homogeneous Equation with Constant Coefficient 154 – 188**

6.1. Solution of differential equation 154-161

6.2. Particular integral 161-162

6.3. Particular integral for some cases 162-188

**7. Homogeneous Linear Equation (Cauchy-Euler’s Equation) 189 – 201**

7.1. Cauchy-euler’s equation 189-191

7.2. Determination of complementery function (C.F.) 191-191

7.3. Particular integral of the function (P.I.) 191-199

7.4. Equation reducible to homogeneous linear form 199-201

8. Simultaneous Differential Equation 202 – 218

8.1. Introduction 202-212

8.2. Simultaneous equation of the form 212-218

**9. Total Differential Equation 219 – 240**

9.1. Pfaffian differential form 219-219

9.2. Pfaffian differential equation 219-219

9.3. Pfaffian differential equation in three variable (Total d.e.) 219-224

9.4. Condition of exactness 224-238

9.5. When the equation is not integrable 238 **10. Partial Differential Equation of First Degree 241 – 255**

10.1.Definition 241-241

10.2. Order of partial differential equation 241-242

10.3. Degree of partial differential equation 242-242

10.4. Linear partial differential equation 242-243

10.5.Nonlinear partial differential equation 243-243

10.6. Formation of partial differential equation 243-254

10.7.Solution of partial differential equation 254-255

**11. Lagrange’s Method 256 – 276**

11.1. Lagrange’s equation 256-256

11.2. General solution of Lagrange’s equation 256-257

11.3. Linear partial differential equation with n independent variable 257-270

11.4. Integral surface passes through the given point 270-276

**12. Nonlinear Partial Differential Equation of First Order 277 – 298**

12.1. Introduction 277-277

12.2.Standard form I 277-283

12.3.Standard form II 283-289

12.4.Standard form III 289-294

12.5.Standard form IV 294-298

**13. Charpit’s Method 299 – 312**

13.1. Introduction 299-299

13.2. Charpit’s auxiliarly equation 299-312

14. Classification of Second Order Partial Differential Equation 313 – 320

14.1. Linear partial differential equation of second order in independent variable 313-314 14.2. Classification of linear partial differential equation of second order in two independent variable. 314-320

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