A First Course in Differential Equations with Modeling Applications (MindTap Course List)
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
11th Edition
ISBN: 9781305965720
Author: Dennis G. Zill
Publisher: Cengage Learning
bartleby

Concept explainers

Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
bartleby

Videos

Textbook Question
Book Icon
Chapter 1.1, Problem 19E

In Problems 19 and 20 verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y = ϕ(x) in each case. Use a graphing utility to obtain the graph of an explicit solution. Give an interval I of definition of each solution ϕ.

19. d X d t = ( X − 1 ) ( 1 − 2 X ) ;   ln ( 2 X − 1 X − 1 ) = t

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 1.1, Problem 18E
Next
Chapter 1.1, Problem 20E
Students have asked these similar questions
No chatgpt pls
19
12

Chapter 1 Solutions

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

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 - Using the concept of net rate introduced in...Ch. 1.3 - Modify the model in Problem 3 for net rate at...Ch. 1.3 - A cup of coffee cools according to Newtons law of...Ch. 1.3 - The ambient temperature Tm in (3) could be a...Ch. 1.3 - Suppose a student carrying a flu virus returns to...Ch. 1.3 - At a time denoted as t = 0 a technological...Ch. 1.3 - Suppose that a large mixing tank initially holds...Ch. 1.3 - Suppose that a large mixing tank initially holds...Ch. 1.3 - What is the differential equation in Problem 10,...Ch. 1.3 - Generalize the model given in equation (8) of this...Ch. 1.3 - Suppose water is leaking from a tank through a...Ch. 1.3 - The right-circular conical tank shown in Figure...Ch. 1.3 - A series circuit contains a resistor and an...Ch. 1.3 - A series circuit contains a resistor and a...Ch. 1.3 - For high-speed motion through the airsuch as the...Ch. 1.3 - A cylindrical barrel s feet in diameter of weight...Ch. 1.3 - After a mass m is attached to a spring, it...Ch. 1.3 - In Problem 19, what is a differential equation for...Ch. 1.3 - A small single-stage rocket is launched vertically...Ch. 1.3 - In Problem 21, the mass m(t) is the sum of three...Ch. 1.3 - By Newtons universal law of gravitation the...Ch. 1.3 - Suppose a hole is drilled through the center of...Ch. 1.3 - Learning Theory In the theory of learning, the...Ch. 1.3 - Forgetfulness In Problem 25 assume that the rate...Ch. 1.3 - Infusion of a Drug A drug is infused into a...Ch. 1.3 - Tractrix A motorboat starts at the origin and...Ch. 1.3 - Reflecting surface Assume that when the plane...Ch. 1.3 - Reread Problem 45 in Exercises 1.1 and then give...Ch. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Prob. 33ECh. 1.3 - Rotating Fluid As shown in Figure 1.3.24(a), a...Ch. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Let It snow The snowplow problem is a classic and...Ch. 1.3 - Population Dynamics Suppose that dP/dt = 0.15 P(t)...Ch. 1.3 - Radioactive Decay Suppose that dA/dt = 0.0004332...Ch. 1.3 - Reread this section and classify each mathematical...Ch. 1 - 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...
Knowledge Booster
Background pattern image
Math
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
SEE MORE TEXTBOOKS
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY