Differential Equations

SYLLABUS- DIFFERENTIAL EQUATIONS,
Unit-I: Second order linear equations, general solution of homogeneous equation, use of known solution to find another, homogeneous equation with constant coefficients, method of undetermined coefficient, variation of parameters.

Unit-II: Series solutions of differential equations, Power series method, Bessel, Legendre and hypergeometric equations, Bessel, Legendre and hypergeometric functions and their properties, convergence, recurrence and generating relations.

Unit-III: Orthogonality of functions, Sturm Liouville Problem, Orthogonality of eigen functions, Reality of eigenvalues, Orthogonality of Bessel functions and Legendre polynomials, Oscillation theory and boundary value problems, Qualitative properties of solutions, Sturm-comparison theorem, regular Sturm- Liouville problem, examples.

Unit-IV: Linear systems, Homogeneous linear system with constant coeficient, Volterra Prey-Predator equations, Non-linear equations, Autonomous system, critical points, stability of linear system, Liapunov direct method, Simple critical
points of non-linear systems.