1550078481-Ordinary_Differential_Equations__Roberts_

Applications of Systems of Equations 483 Physically the critical points (2mr, 0) correspond to the pendulum being at rest (y2 = ...

484 Ordinary Differential Equations and if we assume there is no forcing function (f(t) = 0), then the differential equation (1) ...

Applications of Systems of Equations 485 function. Dividing by mf(t) and letting y 1 = y and y 2 = y', we can rewrite (9) as the ...

486 Ordinary Differential Equations and f, is the length of the pendulum. The x-axis and y-axis form a rectangular coordinate sy ...

Applications of Systems of Equations 487 A spring pendulum has two "natural frequencies." The first frequency WI = VifLo corresp ...

488 Ordinary Differential Equations for (a) A -.5 and (b) A = -1 for the initial conditions Y1(0) = 0 and (i) y 2 (0) = 2.5 and ...

Applications of Systems of Equations 489 (ii) Y1(0) = 2.1, Y2(0) = 0, y3(0) = .05, and y4(0) = 0. (The spring pendulum is set in ...

490 Ordinary Differential Equations EXERCISE 10.8 Let Y1 = y and Y2 = y' and write equation (5) as an equivalent system of two ...

Applications of Systems of Equations 491 EXERCISE 10.9 l. Numerically solve system (2) on the interval [O, 10] for (a) E = .5 an ...

492 Ordinary Differential Equations where the outflow rate from pond A to pond B is r 0 = 70 gal/hr. Thus, the amount of salt in ...

Applications of Systems of Equations 493 The amount of salt in pond A begins to increase first. The amount of salt in pond B beg ...

494 Ordinary Differential Equations Display a graph for the concentration of pollution in all lakes for both cases and compa re ...

Applications of Systems of Equations (x(t), y(t)) -μ 1-μ Figure 10.27 The Restricted Three-Body Problem and Associated Critical ...

496 Ordinary Differential Equations The critical points of system (2) can be found by setting the right-hand-sides of equations ...

Applications of Systems of Equations 497 For μ = .012129 t his equation is (5) z^5 - l.951484z^4 + .9281087z^3 + l.023382z^2 - l ...

498 Ordinary Differential Equations EXERCISES 10.11 Verify that ((1 - 2μ)/2, 0, ±v'3/2, 0) are critical points of system (2). F ...

Appendix A CSODE User's Guide Computer Solutions of Ordinary Differential Equations (CSODE) is a col- lection of six computer pr ...

500 Ordinary Differential Equations is a single precision, floating-point representation for the number 23400000. And 314159E-5, ...

CSODE User's Guide 501 iii POLYRTS J!il[!Jf!I POLYRTS finds all zeros of a polynomial with complex coefficients of degree N wher ...

502 Ordinary Differential Equations iii POLYRTS 181!1 £i POLYRTS finds all zeros of a polynomial with complex coefficients of de ...