( MATHEMATICS, Paper- II ) ORDINARY DIFFERENTIAL EQUATIONS B.Sc 3rd Sem Bihar

Unit

Subject

No. of Lectures

1

Formulation of Differential equations and its order and degree, General, Particular and Singular solutions of differential equations, variables separable, Equations reducible to variables separable, Homogeneous differential equations, Equations reducible to homogeneous form, Exact differential equations and equations reducible to the exact form, Linear differential equations and equations reducible to linear form, Bernoulli equation.

10

2

Differential equations of first order but not of first degree, Singular solutions, Clairaut’s form, Orthogonal Trajectories of family of curves, Wronskian and its properties, Linear differential equation of order greater than one with constant coefficients, Cauchy- Euler Equation, Legendre’s Linear Equation.

10

3

Second order linear differential equations with variable coefficients: Use of a known solution to find another, normal form, method of undetermined coefficient, variation of parameters, Total differential equation in three variables, Simultaneous differential equations.

10

4

Definition of Laplace transform, Existence Theorem, Formulas and Properties of Laplace transform, Laplace transform of special functions viz: Dirac’s delta, Unit step, Periodic, Bessel, Error functions, Inverse Laplace transform, Formulas and Properties of inverse Laplace transform, Convolution theorem, Solution of ordinary differential equation using Laplace transform.

10

Unit

Subject

No. of Lectures

1

Formulation of Differential equations and its order and degree, General, Particular and Singular solutions of differential equations, variables separable, Equations reducible to variables separable, Homogeneous differential equations, Equations reducible to homogeneous form, Exact differential equations and equations reducible to the exact form, Linear differential equations and equations reducible to linear form, Bernoulli equation.

10

2

Differential equations of first order but not of first degree, Singular solutions, Clairaut’s form, Linear differential equation of order greater than one with constant coefficients, Cauchy-Euler Equation, Legendre’s Linear Equation.

10

3

Second order linear differential equations with variable coefficients: Use of a known solution to find another, normal form, method of undetermined coefficient, variation of parameters, Total differential equation in three variables, Simultaneous differential equations.

10