1550078481-Ordinary_Differential_Equations__Roberts_

Answers to Selected Exercises 543 c. En ::; .000004167 d. h ::; .059 b. 3. 5. Taylor Series Improved Fourth-Order Exact Xn Orde ...

544 Ordinary Differential Equations Exercises 2.4.4 Pitfalls of Numerical Methods The given differential equation is linear wit ...

Answers to Selected Exercises 545 The differential equation is nonlinear and f(x, y) = 3xy^113 is continu- ous on the entire pl ...

546 Ordinary Differential Equations Chapter 3 APPLICATIONS OF THE INITIAL VALUE PROBLEM: y' = f(x,y); y(c) = d Exercises 3.1 Cal ...

Answers to Selected Exercises 547 Exercises 3.3 Population Models P(t) = (2.5 x 108 )10 '3~~ 50 where t is the calendar year. 2 ...

548 Ordinary Differential Equations Exercises 3.8 Chemical Reactions l. b. 2 moles/liter b. 3 moles/liter b. 4.5 moles/liter c ...

Answers to Selected Exercises 549 Exercises 4.2 Roots of Polynomials X1 = 1.36881, X2 = -1.68440 + 3.43133i, X3 = -1.68440 - 3. ...

550 Ordinary Differential Equations Exercises 4.4 Nonhomogeneous Linear Equations with Constant Coefficients y = C1 e^2 x + c2e ...

Answers to Selected Exercises 551 a. 3x^2 /2 b. 4xe-^2 x c. - 2x cos v'3x d. e- x + x - l e. ex cos 2x f. ex sin 2x g. 4(cosx- ...

552 Ordinary Differential Equations Exercise s 5.4 The Unit Function and Time-De lay Function 1. a. fi(x)=2u(x)-u(x- 1) b. h(x) ...

Answers to Selected Exercises Chapter 6 APPLICATIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS Exercises 6.1 S ...

554 Ordinary Differential Equations a. qp(t) =EC b. EC c. 0 a. ip(t) = E(l - eRt/L)jR , limt_,+ooip(t) = E/R b. ip(t) = E(Lw s ...

Answers to Selected Exercises Chapter 7 SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS a. linear b. (0, oo) 555 c. (-oo, oo) Be ...

556 Ordinary Differential Equations g. Let u1 = y, u2 = z, and u3 = z '. Then 13. a. ( -oo, oo) c. (i) (-1,2) f. (-oo, oo) u 1 ( ...

Answers to Selected Exercises 557 ( .5 + .5i) V 3 = -.5_~ .5i Al = 5, A2 = 3, A3 = 2, V 1 = ( ~--~:~~~ 2 ) , V2 = (-~:~~:~~) , ...

558 1 5. Ordinary Differential Equations +c,{c'x sinx m + c'xooex (~} cs{e'x cos~ (-! )-,ax sin 4x (~} ~{caxsin4x (-!) +,ax ...

Answers to S elected Exercises Chapter 9 APPLICATIONS OF LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS Exercises 9.1 Coupled Spring- ...

560 a. b. u'= Ordinary Differential Equations -'---(k1 --'---+ k2)u1 - d1u2 --+ --k2u3 m1 m1 m1 U4=^1 ---k2Ul ---k2U3 --d2U4 m ...

Answers to Selected Exercises 561 b. (i) _ -2x -.322888 -4x 1.73580 -x -. 170219 ( .161444J ( -.433951J ( .170219J u - cie - . ...

562 Ordinary Differential Equations Exercises 9.2 Pendulum Systems 7. a. Let u1 = Y1, u2 = y~, u3 = y2, and U4 = Y2· Then 0 1 0 ...