( MATHEMATICS ) DIFFERENTIAL EQUATIONS-I HARYANA B.SC THIRD SEMESTER

Unit

Topics

Contact Hours

I

Basic concepts and genesis of ordinary differential equations, Order and degree of a differential equation, Solutions of differential equations of first order and first degree, Exact differential equations, Integrating factor, First order higher degree equations solvable for x, y and p, Lagrange’s equations, Clairaut’s form and singular solutions. Orthogonal trajectories of one-parameter families of curves in a plane.

12

II

Solutions of linear ordinary differential equations with constant coefficients, linear non-homogeneous differential equations. Linear differential equation of second order with variable coefficients. Method of reduction of order, method of undetermined coefficients, method of variation of parameters. Cauchy-Euler equation.

12

III

Solution of simultaneous differential equations, total differential equations. Genesis of Partial differential equations (PDE), Concept of linear and non linear PDEs. Complete solution, general solution and singular solution of a PDE. Linear PDE of first order. Lagrange’s method for PDEs of the form: P(x ,y, z) p + Q(x, y, z) q = R(x, y, z), where p=∂z/∂x and q=∂z/∂y.

12

IV

Integral surfaces passing through a given curve. Surfaces orthogonal to a given system of surfaces. Compatible systems of first order equations. Charpit’s method, Special types of first order PDEs, Jacobi’s method. Second Order Partial Differential Equations with Constant Coefficients.

12