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Ordinary Differential Equations

Code: MA548 | L-T-P-C: 3-1-0-8

Prerequisites: Nil

First order non-linear differential equations: Existence and Uniqueness problem, Gronwall’s inequality, Peano existence theorem, Picard existence and uniqueness theorem, interval of definition. Second order linear differential equations: general solution for homogeneous equations, superposition of solutions, methods of solution for non-homogeneous problems, undetermined coefficients, variation of parameters, series solutions for ODEs, types of singularity, solution at an ordinary point, solution at a singular point. nth order linear differential equations: system of equations, homogeneous system of equations, fundamental matrix, Abel-Liouville formula, system of non-homogeneous equations, stability of linear systems. Theory of two-point BVP: Green’s functions, properties of Green’s functions, Adjoint and self-adjoint BVP. Strum-Liouville’s problem, orthogonal functions, eigenvalues and eigen functions, completeness of the eigen functions.


  1. Boyce, W. E. and DiPrima, R. C., Elementary Differential Equation and Boundary Value Problems, 7th Edition, John Wiley & Sons (Asia), 2001.
  2. Ross, S. L., Differential Equations, 3rd edition, Wiley 1984.


  1. Simmons, G. F., Differential Equations with Applications and Historical Notes, McGraw Hill, 1991
  2. Coddington, E. A., An Introduction to Ordinary Differential Equations, Prentice- Hall, 1974.
  3. Farlow, S. J., An Introduction to Differential Equations and Their Applications, McGraw-Hill International Editions, 1994.