Differential Equations
Degree and order of a differential equation .Equations of first order and first degree – Variable separable method , Homogeneous and equations reducible to homogeneous form , Linear and equations reducible to linear form.
Exact differential equations and equation which can be made exact using I.F. First order higher degree equations – solvable for x, y, p. Clairaut’s form.
Linear differential equation with constant coefficients, complimentary function and particular integral. Homogeneous linear differential equations with variable coefficient. Simultaneous differential equations.
Linear differential equations of second order- Linear independence of solutions . Solution by transformation of the equations by changing the dependent and independent variable. Factorization of operators. Method of variation of parameters, Method of undetermined coefficients.
Partial differential equations of the first order. Lagrange’s linear equation, Charpit’s general method of solution , homogeneous linear partial differential equations with constant coefficients. Equations reducible to equations with constant coefficients.
1. D.A.Murray, Introductory course on Differential Equations, Orient Longman, 2004
2. I. N. Sneddon, Elements of Partial Differential Equations , TMH, 2001
3. Zafar Ahsan, Differential Equations & their applications, PHI ,New Delhi, 1998.
4. Bansal and Dhami, Differential Equations, vol. I, JPH, 2012.
1. A.R.Forsyth , A Treatise on Differential Equations , Macmillan and Co. Ltd, London, 1997.
2. Frank Ayres, Theory and Problems of Differential Equations, TMH, 2002.
