first order linear ordinary differential equations examples

... pagesdoi:10.1155/2009/141959 Research Article Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations Alexander Domoshnitsky, Abraham Maghakyan, and Roman Shklyar Department ... maximum principles for delaydifferential equations, they can be only interpreted in a corresponding sense as analogs ofclassical ones for ordinary differential equations and do not imply important ... with the cases of ordinary and evenpartial differential equations, do not add so much in problems of existence and uniqueness forboundary value problems with delay differential equations The Azbelev’s

Ngày tải lên: 22/06/2014, 03:20

... 6A First Course in Ordinary Differential Equations 6 Contents 4.2 Linear homogeneous constant coefficients equations 110 A.2 Higher-order linear constant-coefficient equations 157A.3 Higher-order ... differential equations, we need to start with the simplest type ofequations, which are the linear ordinary differential equations Hereafter, referred funda-to simply as linear differential equations ... free eBooks at bookboon.com Trang 11A First Course in Ordinary Differential Equations 11 Linearity and solutions Chapter 1 Linear differential equations and linearly independent solutions In this

Ngày tải lên: 15/01/2021, 09:11

... 6A First Course in Ordinary Differential Equations 6 Contents 4.2 Linear homogeneous constant coefficients equations 110 A.2 Higher-order linear constant-coefficient equations 157A.3 Higher-order ... differential equations, we need to start with the simplest type ofequations, which are the linear ordinary differential equations Hereafter, referred funda-to simply as linear differential equations ... free eBooks at bookboon.com Trang 11A First Course in Ordinary Differential Equations 11 Linearity and solutions Chapter 1 Linear differential equations and linearly independent solutions In this

Ngày tải lên: 15/01/2021, 09:12

... third-order quasi-linear neutral functional differential equations Arch Math 47, 181 –199 (2011) 18 Yildiz, MK, Öcalan, Ö: Oscillation results of higher-order nonlinear neutral delay differential equations ... for second-order superlinear neutral differential equations Abstr Appl Anal 2011, 1 –17 (2011) 13 Li, T, Han, Z, Zhao, P, Sun, S: Oscillation of even-order neutral delay differential equations ... odd-order nonlinear neutral functional differential equations Electron J Diff Equ 23, 1 –12 (2011) 15 Rath, RN, Padhy, LN, Misra, N: Oscillation of solutions of non-linear neutral delay differential

Ngày tải lên: 20/06/2014, 22:20

... 21Second-order ordinary differential equations21 The method of Frobenius 2 The method of Frobenius We consider the second order, linear ordinary differential equation of ordinary differential equations’ ... order, ordinary differential equations and special functions Trang 11Second-order ordinary differential equations11 List of Equations This is a list of the types of equation, and specific examples, ... Trang 1Second-order ordinary differential equations Special functions, Sturm-Liouville theory and transforms Download free books at Trang 2R.S JohnsonSecond-order ordinary differential equations

Ngày tải lên: 13/01/2021, 09:54

... pagesdoi:10.1155/2011/192156 Research Article Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations Jian Zu College of Mathematics, Jilin University, Changchun 130012, ... a periodic solution for second-order ordinary differential equations with some assumption 1 Introduction The study on periodic solutions for ordinary differential equations is a very important branch ... order vector differential equations,” Journal of Di fferential Equations, vol 9, pp 67–85, 1971. 5 H W Knobloch and K Schmitt, “Non-linear boundary value problems for systems of differential equations,”

Ngày tải lên: 14/07/2023, 09:44

... second-order equations The values of y are stored in the first n elements of y, while the first derivatives are stored in the second n elements The right-hand side f is stored in the first n ... vol 27, pp 505–535 16.6 Stiff Sets of Equations As soon as one deals with more than one first-order differential equation, the possibility of a stiff set of equations arises Stiffness occurs in ... all equations are linear with constant coefficients, unfortunately! For the system implicit differencing gives yn+1= yn+ hf(yn+1) (16.6.15) In general this is some nasty set of nonlinear equations

Ngày tải lên: 24/12/2013, 12:16

... integral equations 34 §3.1 Preliminaries from linear algebra 41 §3.2 Linear autonomous first order systems 47 §3.3 General linear first order systems 50 iii Trang 5Chapter 4 Differential equations ... following differential equations into first ordersystems (i) ¨x + t sin( ˙x) = x (ii) ¨x = −y, ¨y = x Trang 17The last system is linear Is the corresponding first order system also linear?Is ... Copyright c Trang 4§1.2 Classification of differential equations 5§1.3 First order autonomous equations 8 §1.5 Qualitative analysis of first order equations 16 §2.2 The basic existence and uniqueness

Ngày tải lên: 31/03/2014, 15:56

... third-order differential equations see 1 20 Various techniques appeared for the investigation of such equations Some of them1,19 make use of the methods developed for the second-order equations ... from the oscillation of a couple of the first-order differential equations Obtained comparison principles essentially simplify the examination of the studied equations 1 Introduction In this paper, ... properties ofE We will compare E with a couple of the first-order delay differential equations in the sense that the oscillation of these equations yields the studied properties ofE 2 Main Results

Ngày tải lên: 21/06/2014, 11:20

... Differential Equations, vol 232, no 1, pp 277–284, 2007 28 P J Torres, Existence and stability of periodic solutions for second-order semilinear differential equations with a singular nonlinearity,” ... by Donal O’Regan We present some recent existence results for second-order singular periodic differential equations. A nonlinear alternative principle of Leray-Schauder type, a well-known fixed ... It is well known that second order singular differential equations describe many problems in the applied sciences, such as the Brillouin focusing system 1 and nonlinear elasticity 2. Therefore,

Ngày tải lên: 21/06/2014, 20:20

... 1fference EquationsVolume 2007, Article ID 40160, 17 pages doi:10.1155/2007/40160 Research Article Necessary Conditions of Optimality for Second-Order Nonlinear Impulsive Differential Equations ... a class of the second-order nonlinear impulsive differential equation in infinite di-mensional spaces Consider the following second-order nonlinear impulsive differential equations: ¨x(t) = A ˙x(t) ... second-order nonlinear impulsive differential equations By reducing wave equation to the customary vector form, Fattorini obtained the maximum principle for time optimal control problem of the semilinear

Ngày tải lên: 22/06/2014, 19:20

... allow superlinear growth of the nonlinearity of f (t, p) in p  Inspired by [21,24,25], in this paper, we investigate the following second-order impul-sive nonlinear differential equations with ... pagesdoi:10.1155/2007/41589 Research Article Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions Chuanzhi Bai and Dandan Yang ... from many authors in recent years Recently, Chen et al in [21] study the following first-order impulsive nonlinear peri-odic boundary value problem: x (t) = f (t,x), t ∈[0,N], t = t1, x t1+

Ngày tải lên: 22/06/2014, 19:20

... fourth order quasilinear functional differential equations, Hiroshima Mathematical Journal 33 (2003), no 3, 297–316 , Oscillation criteria for a class of higher order nonlinear differential ... class of second order quasilinear functionaldifferential equations, Hiroshima Mathematical Journal 27 (1997), no 3, 449–466 Jelena Manojlovi´ : Department... differential equations, Pacific ... OSCILLATION AND NONOSCILLATION THEOREMS FOR A CLASS OF EVEN-ORDER QUASILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS JELENA MANOJLOVI ´ C AND TOMOYUKI TANIGAWA Received 13 November 2005;

Ngày tải lên: 22/06/2014, 21:20

... 1NONLINEAR DIFFERENCE EQUATIONSRAVI P AGARWAL, SAID R GRACE, AND TIM SMITH Received 11 August 2005; Revised 20 March 2006; Accepted 25 April 2006 Some new criteria for the oscillation of first-order ... medium, provided the original work is properly cited 1 Introduction We consider first-order forced nonlinear difference equations of the type Δx(n) + p(n)x(n + 1) + q1(n)x μ(n + 1) = e(n), (1.1) Δx(n) ... that is, the linear case.Section 4is devoted to the study of the oscillatory behavior of (1.3) We also proceed further in this direction and obtain oscillation criteria for second-order equations

Ngày tải lên: 22/06/2014, 22:20

... singular boundary value problem (BVP) for a second-order nonlinear differential tion is studied This BVP is a model in hydrodynamics as well as in nonlinear field theoryand especially in the study ... Trang 1DIFFERENTIAL EQUATIONS: THEORETICAL ANALYSISAND NUMERICAL SIMULATIONS OF GROUND STATES ALEX P PALAMIDES ... emanating u 1=max where u denotes the usual sup-norm ofu on [0, T] On the other hand, in order to prove that the operator Trang 5Furthermore,{ Sρ }is an equicontinuous family sinceProof

Ngày tải lên: 22/06/2014, 22:20

... Trang 1NUMERICAL SOLUTIONSOF ORDINARY DIFFERENTIAL EQUATIONS Trang 2ODEs in Chemical Engineering• The ODEs that occur in Chemical Engineering ... Taylor Series• Accuracy of this solution is dependent on the ‘order’ of the Taylor Series expansion • Need to have the higher order differentials of x(t) to maintain accuracy – may not be available ... the equations are solved one at a time, using the same methods as for single ODEs, Trang 26Solving higher order ODEs• All numerical ODE solution methods are designed for applications to 1st order

Ngày tải lên: 19/03/2015, 08:49

... of ordinary differential equations Trang 8in general with the n-order form∞ P k=0 (tA)kk! = I + tA + (tA)22! + + (tA)kk! + Trang 91.2 Existence and uniqueness theoremsThe existence of the differential ... STABILITY OF ORDINARY DIFFERENTIAL EQUA-TIONS 16 2.1 Lyapunov functions 16 2.2 Strong linear stability 24 2.3 Orbital stability 32 2.4 Bounding functions 33 2.5 Non-autonomous equations ... the other hand, the differential equations are an approximation tothe true equations of motion We will be interested in finding whetherthe solutions of slightly different equations give the same

Ngày tải lên: 23/12/2019, 16:17

... Department of Mathematics Unit 3 Linear Equations Exact Differential Equations Trang 47Slide 11 - 47 Dr Nguyen Huu Tho - Department of Mathematics 2.4 Linear Equations Trang 48Slide 11 - 48 ... DIFFERENTIAL EQUATIONS Lecturer : Dr Nguyễn Hữu Thọ Department of Mathematics - WRU Trang 2Slide 11 - 2 Dr Nguyen Huu Tho - Department of Mathematics Unit 1 Introduction to Differential Equations ... Department of Mathematics Unit 6 Systems of Linear Equations Trang 108Slide 11 - 108 Dr Nguyen Huu Tho - Department of Mathematics 7.2 Systems of Linear Equations with two or three variables Trang

Ngày tải lên: 16/12/2020, 00:10

... Department of Mathematics Unit 3 Linear Equations Exact Differential Equations Trang 47Slide 11 - 47 Dr Nguyen Huu Tho - Department of Mathematics 2.4 Linear Equations Trang 48Slide 11 - 48 ... DIFFERENTIAL EQUATIONS Lecturer : Dr Nguyễn Hữu Thọ Department of Mathematics - WRU Trang 2Slide 11 - 2 Dr Nguyen Huu Tho - Department of Mathematics Unit 1 Introduction to Differential Equations ... Department of Mathematics Unit 6 Systems of Linear Equations Trang 108Slide 11 - 108 Dr Nguyen Huu Tho - Department of Mathematics 7.2 Systems of Linear Equations with two or three variables Trang

Ngày tải lên: 21/03/2021, 18:30

... of ordinary differential equations Trang 8in general with the n-order form∞ P k=0 (tA)kk! = I + tA + (tA)22! + + (tA)kk! + Trang 91.2 Existence and uniqueness theoremsThe existence of the differential ... STABILITY OF ORDINARY DIFFERENTIAL EQUA-TIONS 16 2.1 Lyapunov functions 16 2.2 Strong linear stability 24 2.3 Orbital stability 32 2.4 Bounding functions 33 2.5 Non-autonomous equations ... the other hand, the differential equations are an approximation tothe true equations of motion We will be interested in finding whetherthe solutions of slightly different equations give the same

Ngày tải lên: 07/04/2021, 08:05