Unit 1

First order ODEs, Modelling, Direction Fields, Separable ODEs, Exact ODEs and Integrating Factors, Linear ODEs and Modelling. (Sections: 1.1 to 1.5)

Unit 2

Second Order Differential Equations: Homogeneous and non-homogeneous linear differential equations of second order, Modelling a Spring-Mass System, Euler-Cauchy Equations, Existence and Uniqueness of solutions (statement), Wronskian, Solution by Undetermined Coefficients and Variation of Parameters, Modelling. (Sections 2.1, 2.2, 2.4 to 2.10)

Unit 3

Homogeneous and non-homogeneous Higher Order Linear ODEs, Systems of ODE.
Series Solutions of ODEs: Power Series method, Legendre’s equation and Legendre Polynomials. (Sections 3.1, 3.2, 3.3, 4.1, 5.1 to 5.2)

Unit 4

Extended Power Series method – Frobenius method, Bessel’s equation and Bessel Functions, General Solution. (Sections 5.3, 5.4, 5.5)

Unit 5

Laplace transforms: linearity, first and second shifting theorems, step and Dirac delta functions, Systems of ODEs. (Sections 6.1 to 6.4, 6.7)

Course Outcome
On successful completion of this course, students shall be able to
CO1: analyse and solve linear, separable and exact first-order differential equations
CO2: apply the use concepts of differential equations in modelling engineering problems
CO3: apply and solve first-order and higher order differential equations, analyze trajectories, and comment on the stability of critical points
CO4: apply principles of integration to determine the Laplace transforms for basic functions, derivatives, integrals and periodic functions and find inverse transforms.
CO5: apply Laplace transforms to solve initial value problems.

1. Erwin Kreyszig, Advanced Engineering Mathematics, 10th edition, Wiley.
2. W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 7th edition, Wiley.

1. M.D. Raisinghania, Ordinary and Partial Differential Equations, S Chand Publications.
2. Dennis Zill, A First Course in Differential Equations, Cengage.