S.N

Unit

Content

Domain

Hours as per UGC

1

one

 Geometrical meaning of DE,
 Exact DE, Integrating factors,
 First order higher degree equations solvable for x,y,p,
 Lagrange’s equations,
 Clairaut’s equations,
 Equations reducible to Clairaut’s form,
 Singular solutions,

Must Know

15

2

Two

 Orthogonal trajectories in cartesian coordinates and polar coordinates,
 Self orthogonal family of curves,
 Linear DE with constant coefficients,
 Homogeneous linear ODE,
 Equations reducible to homogeneous,
 Linear DE of second order: Reduction to normal form,
 Transformation of the equation by changing the dependent variable/independent variable,
 Solution by operators of nonhomogeneous linear DE,
 Reduction of order of a DE,
 Method of variations of parameters,
 Method of undetermined coefficients

Must know

15

3

Three

 Ordinary simultaneous DE,
 Solution of simultaneous DE involving operators x (d/dx) or t (d/dt) etc.
 Simultaneous equation of the form dx/P=dy/Q=dz/R,
 Total DE,
 Condition for Pdx+Qdy=Rdz=0 to be exact.
 General method of solving Pdx+Qdy+Rdz=0 by taking one variable constant,
 Method of auxiliary equations

Must know
Nice to know

15
