Probability and complex function: Unit V: Ordinary Differential Equations

Ordinary Differential Equations

Introduction

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An ordinary differential equation is an equation that contains one or several derivatives of an unknown function, which we will call y (x) and which we want to determine from the equation. The equation may also contain y itself as well as given functions and constants.

UNIT - V

ORDINARY DIFFERENTIAL EQUATIONS

High order linear differential equations with constant co-efficients - Method of variation of parameters - Homogenous equation of Euler's and Legendre's type - System of simultaneous linear differential equations with constant co-efficients - Method of undetermined co-efficients.

 

INTRODUCTION

Differential equations are of fundamental importance in engineering mathematics because many physical laws and relations appear mathematically in the form of such equations.

An ordinary differential equation is an equation that contains one or several derivatives of an unknown function, which we will call y (x) and which we want to determine from the equation. The equation may also contain y itself as well as given functions and constants.

The word "Ordinary" distinguishes them from partial differential equations, involving an unknown function of two or more variables and its partial derivatives. In applied mathematics, every geometrical or physical problem when translated into mathematical symbols gives rise to a differential equation. The study of a differential equation in applied mathematics consists of three phases.

(i) Formation of differential equation from the given physical situation, called modelling.

(ii) Solutions of this differential equation, evaluating the arbitrary constants from the given conditions, and

(iii) Physical interpretation of the solution.

 

Probability and complex function: Unit V: Ordinary Differential Equations : Tag: : Introduction - Ordinary Differential Equations

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Related Topics


Ordinary Differential Equations - Introduction

Higher order linear differential equations with constant coefficients

(a) Problems based on r.h.s. of the given differential equation is zero - Solved Example Problems | Ordinary Differential Equations

(b) Problems based on P.I.= 1/f(D) eax ⇒ Replace D by a - Solved Example Problems | Ordinary Differential Equations

(c) Problems based on P.I = 1 / f(D) sin ax or 1 / f(D) cos ax ⇒ Replace D2 by -a2 - Solved Example Problems | Ordinary Differential Equations

(d) problems based on R.H.S = eax + sin ax(or) eax + cos ax - Solved Example Problems | Ordinary Differential Equations

(e) problems based on R.H.S = xn - Solved Example Problems | Ordinary Differential Equations

(f) Problems based on R.H.S. = eax X - Solved Example Problems | Ordinary Differential Equations

(g) problems based on f(x) = x V type - Solved Example Problems | Ordinary Differential Equations

(h) problems based on eax integral e-ax - Solved Example Problems | Ordinary Differential Equations

(i) General ode problems - Solved Example Problems | Ordinary Differential Equations

(i) Problems based on R.H.S = eax + xn + cos ax - Solved Example Problems | Ordinary Differential Equations

Exercise 5.1 (Ordinary Differential Equations) - Problems with Answer

Method of variation of parameters - Ordinary Differential Equations

Problems based on method of variation of parameters - Solved Example Problems | Ordinary Differential Equations

Related Subjects


Probability and complex function

Probability and complex function

MA3303 3rd Semester EEE Dept | 2021 Regulation | 3rd Semester EEE Dept 2021 Regulation