Non-linear ordinary differential equations of particular forms. Riccati's equation -General solution and the solution when one, two or three particular solutions are known. Total Differential equations.

 

Partial differential equation of first order – formulation and classification of partial differential equations, Lagrange’s linear equation, particular forms of non – linear partial differential equations of first order, Charpit’s method. 

 

Linear Partial differential equations with constant coefficients.  Homogeneous and non- Homogeneous equation. 

 

Second order Partial Differential equations – formulation and classification of Second Order Partial Differential equations, Monge’s methods- Canonical forms, classification of Second order Partial differential equations of the type Rr+Ss+Tt+f(x,y,z,p,q)=0 and second order Partial differential equations in more than two independent variables. Method of separation of variables, Laplace, Wave and diffusion  equations..