First Course in Differential Equations (Instructor's)
11th Edition
ISBN: 9781305965775
Author: ZILL
Publisher: CENGAGE L
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Chapter 1.1, Problem 50E
In Problems 49 and 50 the given figure represents the graph of an implicit solution G(x, y) = 0 of a differential equation dy/dx = f(x, y). In each case the relation G(x, y) = 0 implicitly defines several solutions of the DE. Carefully reproduce each figure on a piece of paper. Use different colored pencils to mark off segments, or pieces, on each graph that correspond to graphs of solutions. Keep in mind that a solution ϕ must be a function and differentiable. Use the solution curve to estimate an interval I of definition of each solution ϕ.
FIGURE 1.1.7 Graph for Problem 50
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Chapter 1 Solutions
First Course in Differential Equations (Instructor's)
Ch. 1.1 - In Problems 18 state the order of the given...Ch. 1.1 - In Problems 18 state the order of the given...Ch. 1.1 - In Problems 18 state the order of the given...Ch. 1.1 - In Problems 18 state the order of the given...Ch. 1.1 - In Problems 18 state the order of the given...Ch. 1.1 - In Problems 18 state the order of the given...Ch. 1.1 - In Problems 18 state the order of the given...Ch. 1.1 - In Problems 18 state the order of the given...Ch. 1.1 - In Problems 9 and 10 determine whether the given...Ch. 1.1 - In Problems 9 and 10 determine whether the given...
Ch. 1.1 - In Problems 1114 verify that the indicated...Ch. 1.1 - In Problems 1114 verify that the indicated...Ch. 1.1 - In Problems 1114 verify that the indicated...Ch. 1.1 - In Problems 1114 verify that the indicated...Ch. 1.1 - In Problems 1518 verify that the indicated...Ch. 1.1 - In Problems 1518 verify that the indicated...Ch. 1.1 - In Problems 1518 verify that the indicated...Ch. 1.1 - In Problems 1518 verify that the indicated...Ch. 1.1 - In Problems 19 and 20 verify that the indicated...Ch. 1.1 - In Problems 19 and 20 verify that the indicated...Ch. 1.1 - In Problems 2124 verify that the indicated family...Ch. 1.1 - In Problems 2124 verify that the indicated family...Ch. 1.1 - In Problems 2124 verify that the indicated family...Ch. 1.1 - In Problems 2124 verify that the indicated family...Ch. 1.1 - In Problems 2528 use (12) to verify that the...Ch. 1.1 - In Problems 2528 use (12) to verify that the...Ch. 1.1 - In Problems 2528 use (12) to verify that the...Ch. 1.1 - In Problems 2528 use (12) to verify that the...Ch. 1.1 - Verify that the piecewise-defined function...Ch. 1.1 - In Example 7 we saw that y=1(x)=25x2 and...Ch. 1.1 - In Problems 31-34 find values of m so that the...Ch. 1.1 - In Problems 31-34 find values of m so that the...Ch. 1.1 - In Problems 31-34 find values of m so that the...Ch. 1.1 - In Problems 31-34 find values of m so that the...Ch. 1.1 - In Problems 35 and 36 find values of m so that the...Ch. 1.1 - In Problems 35 and 36 find values of m so that the...Ch. 1.1 - In Problems 3740 use the concept that y = c, x ...Ch. 1.1 - In Problems 3740 use the concept that y = c, x ...Ch. 1.1 - In Problems 3740 use the concept that y = c, x ...Ch. 1.1 - In Problems 3740 use the concept that y = c, x ...Ch. 1.1 - Prob. 41ECh. 1.1 - In Problems 41 and 42 verify that the indicated...Ch. 1.1 - Prob. 43ECh. 1.1 - Make up a differential equation that you feel...Ch. 1.1 - What function do you know from calculus is such...Ch. 1.1 - What function (or functions) do you know from...Ch. 1.1 - The function y = sin x is an explicit solution of...Ch. 1.1 - Discuss why it makes intuitive sense to presume...Ch. 1.1 - In Problems 49 and 50 the given figure represents...Ch. 1.1 - In Problems 49 and 50 the given figure represents...Ch. 1.1 - The graphs of members of the one-parameter family...Ch. 1.1 - Prob. 52ECh. 1.1 - In Example 7 the largest interval I over which the...Ch. 1.1 - In Problem 21 a one-parameter family of solutions...Ch. 1.1 - Discuss, and illustrate with examples, how to...Ch. 1.1 - The differential equation x(y)2 4y 12x3 = 0 has...Ch. 1.1 - Prob. 57ECh. 1.1 - Find a linear second-order differential equation...Ch. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Consider the differential equation dy/dx = y(a ...Ch. 1.1 - Consider the differential equation y = y2 + 4. (a)...Ch. 1.2 - In Problems 1 and 2, y = 1/(1 + c1ex) is a...Ch. 1.2 - In Problems 1 and 2, y = 1/(1 + c1ex) is a...Ch. 1.2 - In Problems 36, y = 1/(x2 + c) is a one-parameter...Ch. 1.2 - In Problems 36, y = 1/(x2 + c) is a one-parameter...Ch. 1.2 - In Problems 36, y = 1/(x2 + c) is a one-parameter...Ch. 1.2 - In Problems 36, y = 1/(x2 + c) is a one-parameter...Ch. 1.2 - In Problems 710, x = c1 cos t + c2 sin t is a...Ch. 1.2 - Prob. 8ECh. 1.2 - In Problems 710, x = c1 cos t + c2 sin t is a...Ch. 1.2 - In Problems 710, x = c1 cos t + c2 sin t is a...Ch. 1.2 - In Problems 1114, y = c1ex + c2ex is a...Ch. 1.2 - In Problems 1114, y = c1ex + c2ex is a...Ch. 1.2 - In Problems 1114, y = c1ex + c2ex is a...Ch. 1.2 - In Problems 1114, y = c1ex + c2ex is a...Ch. 1.2 - In Problems 15 and 16 determine by inspection at...Ch. 1.2 - In Problems 15 and 16 determine by inspection at...Ch. 1.2 - In Problems 1724 determine a region of the...Ch. 1.2 - In Problems 1724 determine a region of the...Ch. 1.2 - In Problems 1724 determine a region of the...Ch. 1.2 - In Problems 1724 determine a region of the...Ch. 1.2 - In Problems 1724 determine a region of the...Ch. 1.2 - In Problems 1724 determine a region of the...Ch. 1.2 - In Problems 1724 determine a region of the...Ch. 1.2 - In Problems 1724 determine a region of the...Ch. 1.2 - In Problems 2528 determine whether Theorem 1.2.1...Ch. 1.2 - In Problems 2528 determine whether Theorem 1.2.1...Ch. 1.2 - In Problems 2528 determine whether Theorem 1.2.1...Ch. 1.2 - In Problems 2528 determine whether Theorem 1.2.1...Ch. 1.2 - (a) By inspection find a one-parameter family of...Ch. 1.2 - (a) Verify that y = tan (x + c) is a one-parameter...Ch. 1.2 - (a) Verify that y = 1 /(x + c) is a one-parameter...Ch. 1.2 - (a) Show that a solution from the family in part...Ch. 1.2 - (a) Verify that 3x2 y2 = c is a one-parameter...Ch. 1.2 - (a) Use the family of solutions in part (a) of...Ch. 1.2 - In Problems 3538 the graph of a member of a family...Ch. 1.2 - In Problems 3538 the graph of a member of a family...Ch. 1.2 - In Problems 3538 the graph of a member of a family...Ch. 1.2 - In Problems 3538 the graph of a member of a family...Ch. 1.2 - In Problems 3944, y = c1 cos 2x + c2 sin 2x is a...Ch. 1.2 - In Problems 3944, y = c1 cos 2x + c2 sin 2x is a...Ch. 1.2 - In Problems 3944, y = c1 cos 2x + c2 sin 2x is a...Ch. 1.2 - In Problems 3944, y = c1 cos 2x + c2 sin 2x is a...Ch. 1.2 - In Problems 3944, y = c1 cos 2x + c2 sin 2x is a...Ch. 1.2 - In Problems 3944, y = c1 cos 2x + c2 sin 2x is a...Ch. 1.2 - Find a function whose graph at each point (x, y)...Ch. 1.2 - Prob. 46ECh. 1.2 - Consider the initial-value problem y = x 2y, y(0)...Ch. 1.2 - Show that x=0y1t3+1dt is an implicit solution of...Ch. 1.2 - Prob. 49ECh. 1.2 - Suppose that the first-order differential equation...Ch. 1.2 - The functions y(x)=116x4, x and...Ch. 1.3 - Under the same assumptions that underlie the model...Ch. 1.3 - The population model given in (1) fails to take...Ch. 1.3 - 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In Problems 1 and 2 fill in the blank and then...Ch. 1 - In Problems 1 and 2 fill in the blank and then...Ch. 1 - In Problems 3 and 4 fill in the blank and then...Ch. 1 - In Problems 3 and 4 fill in the blank and then...Ch. 1 - In Problems 5 and 6 compute y and y and then...Ch. 1 - In Problems 5 and 6 compute y and y and then...Ch. 1 - In Problems 712 match each of the given...Ch. 1 - In Problems 712 match each of the given...Ch. 1 - In Problems 712 match each of the given...Ch. 1 - In Problems 712 match each of the given...Ch. 1 - In Problems 712 match each of the given...Ch. 1 - In Problems 712 match each of the given...Ch. 1 - In Problems 13 and 14 determine by inspection at...Ch. 1 - In Problems 13 and 14 determine by inspection at...Ch. 1 - In Problems 15 and 16 interpret each statement as...Ch. 1 - In Problems 15 and 16 interpret each statement as...Ch. 1 - (a) Give the domain of the function y = x2/3. (b)...Ch. 1 - (a) Verify that the one-parameter family y2 2y =...Ch. 1 - The function y = x 2/x is a solution of the DE xy...Ch. 1 - Suppose that y(x) denotes a solution of the...Ch. 1 - A differential equation may possess more than one...Ch. 1 - What is the slope of the tangent line to the graph...Ch. 1 - In Problems 2326 verify that the indicated...Ch. 1 - In Problems 2326 verify that the indicated...Ch. 1 - In Problems 2326 verify that the indicated...Ch. 1 - In Problems 2326 verify that the indicated...Ch. 1 - In Problems 2730 use (12) of Section 1.1 to verify...Ch. 1 - In Problems 2730 use (12) of Section 1.1 to verify...Ch. 1 - In Problems 2730 use (12) of Section 1.1 to verify...Ch. 1 - In Problems 2730 use (12) of Section 1.1 to verify...Ch. 1 - In Problems 3134 verify that the indicated...Ch. 1 - In Problems 3134 verify that the indicated...Ch. 1 - In Problems 3134 verify that the indicated...Ch. 1 - In Problems 3134 verify that the indicated...Ch. 1 - In Problems 3538, y = c1e3x + c2ex 2x is a...Ch. 1 - In Problems 3538, y = c1e3x + c2ex 2x is a...Ch. 1 - In Problems 3538, y = c1e3x + c2ex 2x is a...Ch. 1 - In Problems 3538, y = c1e3x + c2ex 2x is a...Ch. 1 - The graph of a solution of a second-order...Ch. 1 - A tank in the form of a right-circular cylinder of...
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