First Order Differential Equations : Order and degree of a differential equation, separable differential equations, 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 : Solution of Linear homogeneous and non-homogeneous differential equations of higher order with constant coefficients and with variable coefficients, Methods of variation of parameters.
Differential operator method. 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.