Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th
11th Edition
ISBN: 9781305965737
Author: Dennis G. Zill
Publisher: Brooks Cole
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Textbook Question
Chapter 2.3, Problem 26E
In Problems 25–36 solve the given initial-value problem. Give the largest interval I over which the solution is defined.
26.
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Chapter 2 Solutions
Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th
Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...
Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 13 and 14 the given figure represents...Ch. 2.1 - In Problems 13 and 14 the given figure represents...Ch. 2.1 - In parts (a) and (b) sketch isoclines f(x, y) = c...Ch. 2.1 - (a) Consider the direction field of the...Ch. 2.1 - Consider the autonomous first-order differential...Ch. 2.1 - Consider the autonomous first-order differential...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - Prob. 28ECh. 2.1 - In Problems 29 and 30 consider the autonomous...Ch. 2.1 - In Problems 29 and 30 consider the autonomous...Ch. 2.1 - Consider the autonomous DE dy/dx = (2/)y sin y...Ch. 2.1 - A critical point c of an autonomous first-order DE...Ch. 2.1 - Suppose that y(x) is a nonconstant solution of the...Ch. 2.1 - Prob. 34ECh. 2.1 - Using the autonomous equation (2), discuss how it...Ch. 2.1 - Prob. 36ECh. 2.1 - Suppose the autonomous DE in (2) has no critical...Ch. 2.1 - Population Model The differential equation in...Ch. 2.1 - Population Model Another population model is given...Ch. 2.1 - Terminal Velocity In Section 1.3 we saw that the...Ch. 2.1 - Suppose the model in Problem 40 is modified so...Ch. 2.1 - Chemical reactions When certain kinds of chemicals...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 29 and 30 proceed as in Example 5 and...Ch. 2.2 - In Problems 29 and 30 proceed as in Example 5 and...Ch. 2.2 - In Problems 3134 find an explicit solution of the...Ch. 2.2 - In Problems 3134 find an explicit solution of the...Ch. 2.2 - In Problems 3134 find an explicit solution of the...Ch. 2.2 - In Problems 3134 find an explicit solution of the...Ch. 2.2 - (a) Find a solution of the initial-value problem...Ch. 2.2 - Find a solution of xdydx=y2y that passes through...Ch. 2.2 - Find a singular solution of Problem 21. Of Problem...Ch. 2.2 - Show that an implicit solution of...Ch. 2.2 - Often a radical change in the form of the solution...Ch. 2.2 - Often a radical change in the form of the solution...Ch. 2.2 - Often a radical change in the form of the solution...Ch. 2.2 - Often a radical change in the form of the solution...Ch. 2.2 - Every autonomous first-order equation dy/dx = f(y)...Ch. 2.2 - (a) The autonomous first-order differential...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - In Problems 43 and 44 we saw that every autonomous...Ch. 2.2 - Prob. 54ECh. 2.2 - Find a function whose square plus the square of...Ch. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 1-24 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - Prob. 22ECh. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 3740 proceed as in Example 6 to solve...Ch. 2.3 - In Problems 3740 proceed as in Example 6 to solve...Ch. 2.3 - In Problems 3740 proceed as in Example 6 to solve...Ch. 2.3 - In Problems 3740 proceed as in Example 6 to solve...Ch. 2.3 - In Problems 41 and 42 proceed as in Example 6 to...Ch. 2.3 - In Problems 41 and 42 proceed as in Example 6 to...Ch. 2.3 - In Problems 43 and 44 proceed as in Example 7 and...Ch. 2.3 - Prob. 44ECh. 2.3 - In Problems 45 and 46 proceed as in Example 7 and...Ch. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Reread Example 4 and then find the general...Ch. 2.3 - Reread the discussion following Example 5....Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - In determining the integrating factor (3), we did...Ch. 2.3 - Prob. 56ECh. 2.3 - Radioactive Decay Series The following system of...Ch. 2.3 - Heart Pacemaker A heart pacemaker consists of a...Ch. 2.3 - Prob. 61ECh. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In problems 2126 slove the given initial-value...Ch. 2.4 - In Problem 2126 solve the given initial-value...Ch. 2.4 - In problems 2126 solve the given intial-value...Ch. 2.4 - In Problems 2126 solve the given initial-value...Ch. 2.4 - In Problems 2126 solve the given initial-value...Ch. 2.4 - In Problems 2126 solve the given initial-value...Ch. 2.4 - In Problems 27 and 28 find the value of k so that...Ch. 2.4 - In Problems 27 and 28 find the value of k so that...Ch. 2.4 - In Problems 29 and 30 verify that the given...Ch. 2.4 - In Problems 29 and 30 verify that the given...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 37 and 38 solve the given...Ch. 2.4 - In Problems 37 and 38 solve the given...Ch. 2.4 - (a) Show that a one-parameter family of solutions...Ch. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Discuss how the functions M(x, y) and N(x, y) can...Ch. 2.4 - Differential equations are sometimes solved by...Ch. 2.4 - True or False: Every separable first-order...Ch. 2.4 - Falling Chain A portion of a uniform chain of...Ch. 2.5 - Each DE in Problems 114 is homogeneous. In...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 1-10 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 1-10 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 1114 solve the given initial-value...Ch. 2.5 - In Problems 1114 solve the given initial-value...Ch. 2.5 - In Problems 1114 solve the given initial-value...Ch. 2.5 - In Problems 1114 solve the given initial-value...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 21 and 22 solve the given...Ch. 2.5 - In Problems 21 and 22 solve the given...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - dydx=cos(x+y), y(0) = /4Ch. 2.5 - In Problems 29 and 30 solve the given...Ch. 2.5 - Explain why it is always possible to express any...Ch. 2.5 - Put the homogeneous differential equation...Ch. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - The differential equation dy/dx = P(x) + Q(x)y +...Ch. 2.5 - Determine an appropriate substitution to solve...Ch. 2.5 - Falling Chain In Problem 45 in Exercises 2.4 we...Ch. 2.5 - Population Growth In the study of population...Ch. 2.6 - In Problems 1 and 2 use Eulers method to obtain a...Ch. 2.6 - In Problems 1 and 2 use Eulers method to obtain a...Ch. 2.6 - In Problems 3 and 4 use Eulers method to obtain a...Ch. 2.6 - In Problems 3 and 4 use Eulers method to obtain a...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2 - Answer Problems 112 without referring back to the...Ch. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - In Problems 13 and 14 construct an autonomous...Ch. 2 - The number 0 is a critical point of the autonomous...Ch. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Classify each differential equation as separable,...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - Prob. 21RECh. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 2730 express the solution of the given...Ch. 2 - In Problems 2730 express the solution of the given...Ch. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - In Problems 31 and 32 solve the given...Ch. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - (a) Without solving, explain why the initial-value...Ch. 2 - (a) Find an implicit solution of the initial-value...Ch. 2 - Prob. 37RECh. 2 - Use Eulers method with step size h = 0.1 to...
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- 1 5. [20 points] Solve (x² +y)dx+ 3 dy 0arrow_forwardQ. 67-75 Solve the initial value problems. dy 67. 2 – 7, y(2) = 0 dx 68. 10 - x, y(0) = -1 dx dy 69. - + x, > 0; y(2) = 1 dx 1-² dy 70. == 9x² - 4x + 5, y(-1) = 0 dx dy 71. = 3x-2/3, y(-1) = -5 dx dy 1 72. - y (4) = 0 dx 2Vx ds 73. = 1 + cost, s (0) = 4 dt 74. = cost + sint, s(7) = 1 -π sin 70, 7(0) = 0 1. / 126 + = = ds dt dr 75. d0 Evaluate the integrals in Exercises 13-36. 13. ·/₁ V3-2s ds 14. (2x + 1)³ dx Area In Exercises 37-42, fine x-axis. |37. y = -x − 2x, - 38. y = 3x²-3, -25 39. y=x²-3x² + 2 40. y = x² - 4x. -2 41. y = x¹/³, -1 s 42. y = x¹/3 - x, - 9. (a) Find the termi is (1, -2). (b) Find the initi point is (5, 0. 10. (a) Find the terr is (2, -1). (b) Find the ter point is (-2 11-12 Perform the and w. 11. u = 3i - k, v (a) w - v (c) -v - 2w (e) -8(v + w 12. u = (2,-1,3 (a) u - warrow_forward
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