Non-Homogeneous Second Order Differential Equation.

Slides:

Advertisements

Similar presentations

SECOND-ORDER DIFFERENTIAL EQUATIONS

Advertisements

CHAPTER 5 Higher-Order Linear Differntial Equations Second-order DE: Second-order linear DE: Note: A,B,C,F function of x only Second-order homogeneous.

Ch 3.6: Variation of Parameters

Differential Equation

Differential Equations MTH 242 Lecture # 11 Dr. Manshoor Ahmed.

A second order ordinary differential equation has the general form

Ch 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients

Ch 5.1: Review of Power Series Finding the general solution of a linear differential equation depends on determining a fundamental set of solutions of.

7/4/2015 Cauchy – Euler’s Equations Chapter /4/2015 Cauchy – Euler’s Equations Chapter 5 2.

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

Method Homogeneous Equations Reducible to separable.

II. System of Non-Homogeneous Linear Equations Coefficient Matrix Matrix form Of equations Guiding system （1）（1）

Additional Topics in Differential Equations

Nonhomogeneous Linear Differential Equations

Math 3120 Differential Equations with Boundary Value Problems

Variation of Parameters Method for Non-Homogeneous Equations.

Fin500J Topic 6Fall 2010 Olin Business School 1 Fin500J: Mathematical Foundations in Finance Topic 6: Ordinary Differential Equations Philip H. Dybvig.

Non-Homogeneous Equations

Copyright © Cengage Learning. All rights reserved. 17 Second-Order Differential Equations.

Differential Equations MTH 242 Lecture # 13 Dr. Manshoor Ahmed.

Section 4.4 Undetermined Coefficients— Superposition Approach.

First-Order Differential Equations Part 1

Mathe III Lecture 4 Mathe III Lecture 4 Mathe III Lecture 4 Mathe III Lecture 4.

Chapter 21 Exact Differential Equation Chapter 2 Exact Differential Equation.

Variation of Parameters

Antiderivatives. Indefinite Integral The family of antiderivatives of a function f indicated by The symbol is a stylized S to indicate summation 2.

Nonhomogeneous Linear Differential Equations (Part 2)

6.1 Antiderivatives and Indefinite Integration Objectives: 1.) Understand the concept of a antiderivative 2.) Use differentiation rules to produce and.

Antiderivatives and Indefinite Integration. 1. Verify the statement by showing that the derivative of the right side equals the integrand of the left.

Mathe III Lecture 7 Mathe III Lecture 7. 2 Second Order Differential Equations The simplest possible equation of this type is:

Nonhomogeneous Linear Systems Undetermined Coefficients.

12/19/ Non- homogeneous Differential Equation Chapter 4.

Second-Order Differential

Math 3120 Differential Equations with Boundary Value Problems

Differential Equations Linear Equations with Variable Coefficients.

Existence of a Unique Solution Let the coefficient functions and g(x) be continuous on an interval I and let the leading coefficient function not equal.

Integration The Converse of Differentiation. If the curve passes through (1, -2), find the equation of the curve. The curve passes through (1,-2) Is a.

Section 4.5 Undetermined coefficients— Annhilator Approach.

 y’ = 3x and y’ = x are examples of differential equations  Differential Form dy = f(x) dx.

Differential Equations MTH 242 Lecture # 09 Dr. Manshoor Ahmed.

Chapter 21 Exact Differential Equation Chapter 2 Exact Differential Equation.

Chapter 2 Solvable Equations. Sec 2.1 – 1 st Order Linear Equations  First solvable class of equations  The equation must be able to be expressed in.

A Differential Equation is said to be linear if the dependent variable and its differential coefficient occur in it in the first degree only and are not.

MAT 3237 Differential Equations Section 3.4 Undetermined Coefficients Part II

1 Chapter 5 DIFFERENCE EQUATIONS. 2 WHAT IS A DIFFERENCE EQUATION? A Difference Equation is a relation between the values y k of a function defined on.

Differential Equations MTH 242 Lecture # 28 Dr. Manshoor Ahmed.

3/12/20161differential equations by Chtan (FYHS-Kulai)

Section 4.7 Variation of Parameters. METHOD OF VARIATION OF PARAMETERS For a second-order linear equation in standard form y″ + Py′ + Qy = g(x). 1.Find.

Formation of Partial Differential equations Partial Differential Equation can be formed either by elimination of arbitrary constants or by the elimination.

Differential Equations MTH 242 Lecture # 08 Dr. Manshoor Ahmed.

Section 9.4 – Solving Differential Equations Symbolically Separation of Variables.

Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients

First order non linear pde’s

A second order ordinary differential equation has the general form

MAE 82 – Engineering Mathematics

Class Notes 8: High Order Linear Differential Equation Non Homogeneous

Class Notes 5: Second Order Differential Equation – Non Homogeneous

Section Euler’s Method

Ch 4.4: Variation of Parameters

Systems of Differential Equations Nonhomogeneous Systems

Boyce/DiPrima 9th ed, Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients Elementary Differential Equations and Boundary Value Problems,

6.1: Antiderivatives and Indefinite Integrals

General Solution – Homogeneous and Non-Homogeneous Equations

Boyce/DiPrima 9th ed, Ch 3.6: Variation of Parameters Elementary Differential Equations and Boundary Value Problems, 9th edition, by William E. Boyce.

Ch 3.7: Variation of Parameters

73 – Differential Equations and Natural Logarithms No Calculator

Solve the differential equation using the method of undetermined coefficients. y " + 4y = e 3x 1. {image}

Solve the differential equation using the method of undetermined coefficients. y " + 9y = e 2x {image}

PARTIAL DIFFERENTIAL EQUATIONS

Presentation transcript:

Non-Homogeneous Second Order Differential Equation

We find the general solution of the homogeneous equation as before

Find a particular solution to the non homogeneous equation. This solution is called the particular integral and looks similar to f(x) The general solution of the non-homogeneous differential equation is the sum of the complementary function and the particular integral

How to find the particular integral

Complementary Function

Particular Integral equate coefficients

The general solution of the non-homogeneous differential equation is the sum of the complementary function and the particular integral

Complementary Function

Particular Integral equate coefficients

The general solution of the non-homogeneous differential equation is the sum of the complementary function and the particular integral

Complementary Function

Particular Integral

Complementary Function

Particular Integral

Complementary Function

Particular Integral

Complementary Function

Particular Integral

Product and Sum Rule