Table of Contents

Chapter I: Differential Equations of First Order and First Degree

• Introduction
• Definitions
• Differential Equations of First Order and First Degree
• Method of Separation of Variables
• Homogeneous Equations
• Equations Reducible to Homogeneous Form
• Linear Equations
• Equations Reducible to Linear Form
• Exact Differential Equation
• Integrating Factors for Mdx + Ndy = 0
• Change of Variables

Chapter II: Differential Equations of the First Order but not of the First Degree

• Introduction
• Equations Solvable for p
• Equations Solvable for y
• Equations Solvable for x
• Clairaut’s Equation

Chapter III: Singular Solution and Orthogonal Trajectories

• Geometrical Significance of Solutions
• Singular Solutions
• Trajectories
• Orthogonal Trajectories in Cartesian Coordinates
• Orthogonal Trajectories in Polar Form

Chapter IV: Higher Order Linear Differential Equations with Constant Coefficients

• Higher Order Linear Equations
• Auxiliary Equations
• Particular Integrals by Inverse Operator
• Evaluation of Exponential Functions
• Evaluation of Trigonometric Functions
• Evaluation of Polynomial Functions
• Particular Integral for Non-linear Denominators

Chapter V: Homogeneous Linear Equations with Variable Coefficients

• Introduction
• Equations Reducible to Homogeneous Form

Chapter VI: Simultaneous Differential Equations

• Linear System of Equations
• Simultaneous Differential Equations of First Order

Chapter VII: Total Differential Equations

• Total Differential Equations
• Condition for Integrability
• Methods of Solution
• Solution of Non-integrable Equations
• Geometrical Interpretation

Chapter VIII: Second Order Differential Equations with Variable Coefficients

• Introduction
• Complementary Function
• Removal of First Derivative (Normal Form)
• Change of Independent Variables
• Variation of Parameters
• Factorisation of Operator

Chapter IX: Laplace Transforms

• Introduction
• General Properties
• Common Laplace Transforms
• Laplace Transform of Derivatives and Integrals
• Transform of tⁿf(t) and f(t)/t
• Periodic Functions
• Special Functions
• Inverse Laplace Transform
• Convolution Theorem

Chapter X: Applications to Differential Equations

Chapter XI: Applications to Integral Equations

Authors

• Prof. C.M. Prasad
• Paresh Sanat
• Dr. Kirti Jaiswal
• Sugrew Singh

Publisher

Ankita Publication, Gorakhpur