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Syllabus | B.Sc (Non- Medical) | Title-Ordinary Differential Equations (Code-09010202)

Title-Ordinary Differential Equations (Code-09010202)

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 non-homogeneous 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

     Books Recommended:

  1. Codington, E.A. Introduction to Differential Equations.
  2. Ross, S.L. Differential Equations. New York: John Wiley.
  3. Rai, B. and  D.P. Chaudhary. Ordinary Differential Equations. New Delhi  Narosa, Publishing House