# Differential Equations

## Application of LCR Circuit

Application of LCR Circuit: Here, we consider the Application of LCR Circuit containing a source, resistors, inductors and capacitors. Before discussing the formation of differential equation for the circuits, let us discuss the υ-i relationships for basic network elements. Resistor: The resistor shown in Fig. 11.1(a) has the following relation between voltage and current. where …

## Non Homogeneous Differential Equation

Non Homogeneous Differential Equation: Now let us consider the following Non Homogeneous Differential Equation, where the coefficients a0, a1, … an are constants, and f(t) is a function of me. The general solution may be written where xc is the complementary function, and xp is the particular integral. Since xc is the general solution of …

## Homogeneous Linear Differential Equations

Homogeneous Linear Differential Equations: Consider an nth order homogeneous linear differential equations with constant coefficients, where a0, a1 … an are real constants. Now we shall find the solution of Eq. 11.11 of the form x = emt. By assuming that x = emt is a solution for certain m, we have Substituting in Eq. 11.11, …

## Differential Equations Solutions and Basic Concepts

Differential Equations Solutions and Basic Concepts: Differential Equations Solutions and Basic Concepts which denote rates of change, occur in various branches of science and engineering. We make use of differential equations, for example, to determine the motion of a rocket or a satellite, to determine the charge or current in an electric circuit, or to …

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