Second order linear equations with ordinary points – Legendre equation and Legendre polynomials – Second order equations with regular singular points – Bessel equation.

Systems of first order equations – existence and uniqueness theorem – Fundamental matrix

Non-homogeneous linear systems – linear systems with constant coefficients – linear systems with periodic co-efficient.

Successive approximation – Picard’s theorem - Non-uniqueness of solution – Continuation and dependence on initial conditions, Existence of solutions in the large –Existence and uniqueness of solutions of systems.

Sturm’s comparison theorem – Elementary linear oscillations. Comparison theorem of Hille-Winter – oscillations of x1 =a(t)x(t) - Elementary non-linear oscillation.