This book is designed to serve as a useful text book for the undergaraduate students of Mathematics.
Unit –1 : Introduces the basic concepts and solving of the first order and first degree differential equations. Exact differential equations - integrating factors, linear differential equations, first order and higher degree differential equations are introduced in this chapter.
Unit – 2 : The higher order linear differential equations are discussed in this unit. Solution of homogeneous linear differential equations P(D)y= Q(x) with constant coefficients by means of polynomial operators when Q(x) = bxk, beax, eax V, b cos ax, b sin ax are discussed.
Unit – 3 : The methods of solving the equations by the method of undetermined coefficients, solution of homogeneous linear differential equations with constant coefficients, method of variation of parameters, linear differential equations with non-constant coefficients – The Cauchy-Euler equations are introduced in this unit.
Unit – 4 : The method of forming partial differential equations and methods of solving partial differential equations are discussed. Methods of solving non-linear equations of first order, Charpit’s method, non-homogeneous linear partial differential equations and separation of variables are discussed in this chapter.
UNIT - I
1. Differential Equations of the First Order and of the First Degree
2. Total Differential Equations
3. Differential Equations of the First Order but not of First Degree Practicals
UNIT - II
4. Higher Order Linear Differential Equations
5. Linear Differential Equatiions with Constant Coefficients Practicals
UNIT - III
6. Method of Variations of Parameters
7. Method of Undetermined Coefficients
8. Linear Differential Equations with Non-constant Coefficients-Cauchy-Euler Differential Equations
UNIT - IV
9. Partial Differential Equations