Differential Equations

SYLLABUS- DIFFERENTIAL EQUATIONS,
Differential Equations: Introduction of Differential equations, Order and Degree of Differential Equations, Complete primitive (general solution, particular solution and singular solutions), Existence and uniqueness of the solution dy/dx= f(x,y).
First Order Differential Equations: Differential equations of first order and first degree, Separation of variables, Homogeneous Equations, Exact Equations, Integrating Factor, Linear Equation, Equation of First order but not of first degree, Various methods of solution, Clairaut’s form, Singular solutions, Trajectory, Orthogonal Trajectory, Self-
Orthogonal family of Curves.
Linear Differential Equations: Linear equations with constant coefficients, Complementary function, Particular integral, Working rule for finding solution, Homogeneous linear equations.
Miscellaneous Equations: Simultaneous differential equations, Differential equations of the form dx/P= dy/Q= dz/R where P, Q, R are functions of x, y, z. Exact differential equations, Total differential equations, Series solutions of differential equations, Linear differential equations of second order with variable coefficients.
Applications: Initial and boundary value problems, Simple applications of differential equations of first order.