First Order Differential Equations : Order and degree of a differential equation, Homogeneous differential equations, equations reducible to Homogeneous differential equations, Exact differential equations. Linear differential equations and equations reducible to linear differential equations.
Higher Order Differential Equations : Wronskian, Solution of Linear homogeneous and non-homogeneous differential equations of higher order with constant coefficients and with variable coefficients, Differential Operator Method, Method of variation of parameters.
Higher Order Differential Equations : Linear non-homogeneous differential equations with variable coefficients, Euler’s Cauchy method.
Series Solution of Differential Equation : Regular point, ordinary point, Power Series method, Forbinuous method, Bessel, Legendre and Bessel Equations. Legendre and Bessel functions and their properties, recurrence relations, orthogonality, Rodrigue’s formula.