1550078481-Ordinary_Differential_Equations__Roberts_

CSODE User's Guide 523 o;; SOLVESYS lf!il!Jlf.3 Enter the interval of integration [a, b[ and the initial value c. N= 2 •=L 0 _ b ...

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Appendix B PORTRAIT User's Guide PORTRAIT is a computer program written in Microsoft Visual Basic 6 designed to execute in the M ...

526 Ordinary Differential Equations are all six digit, single precision, floating-point representations for 1r. If the E's in th ...

PORTRAIT User's Guide EXAMPLE Solving Two Initial Value Problems for an Autonomous, Two Component System 527 Use PORTRAIT to sol ...

528 Ordinary Differential Equations ii Computer Solution of Ordma1y 011ferenhal Equations by Charles Roberts 1!11!1 Ei I RUN i i ...

PORTRAIT User's Guide 529 ii PORTRAIT l!liliJf!3 Enter the system defining functions Fl. F2 y'l = Fl = lY1·.5'y1•y2. Enter the n ...

530 Ordinary Differential Equations The first option, Graph solution of one or both components, is already selected, so we click ...

PORTRAIT User's Guide 531 The solution values of the component yl (the prey population) decrease from the initial value of 5 at ...

532 Ordinary Differential Equations .. PORTRAIT 1!!1001£3 Enter lh'n~yttem definin'g functions Fl. F2 Enter the number of initia ...

PORTRAIT User's Guide 533 Substituting this expression for y into the second equatio n of (5), we see x must satisfy 2 2 1 2 8x- ...

534 Ordinary Differential Equations We chose the interval of integration to be small enough so that this trajec- tory did not to ...

PORTRAIT User's Guide 535 Next, we generated solutions to system (4) which corresponded to the ini- tial conditions (iv) x(O) = ...

536 Ordinary Differential Equations ;;; PORTRAIT l!!iliJl!J Enter the SJitem defining functions Fl , F2 Enter the numbe1 of init ...

Appendix C Laplace Transforms Function (Inverse Transform) f(x) = .c-^1 (F(s)) 1 xn, n a positive integer sin bx cos bx sinhbx c ...

538 Ordinary Differential Equations Laplace transforms Function Transform f(x) F(s) = .C[f(x)] f(cx), c>O ~F(~) c c f' sF(s) ...

Answers to Selected Exercises Chapter 1 INTRODUCTION Exercises 1.2 D e finit ions a n d Terminology Linear or Order Nonlinear 1 ...

540 Ordinary Differential Equations Exercises 1.3 Solutions and Problems a. y = 2x ln x / ln 2 b. No unique solution. There ar ...

Answers to Selected Exercises 541 then y(x) _, +oo as x _, +oo. If a solution is negative for x > 0, then y(x) _, -oo as x _, ...

542 Ordinary Differential Equations y = 1 + ~ ln 3 + ~ ln I x - 1 1 · ( 1, oo) 2 2 x+l ' y = -ln I cos x i ; (-7r / 2, 7r / 2 ...