 9.1: Which of the following differential equations are linear? Determine...
 9.2: Find a value of c such that y = x 2 + ecx is a solution of 2y + y = x.
 9.3: In Exercises 36, solve using Separation of Variables. 3. dy dt = t 2y3
 9.4: In Exercises 36, solve using Separation of Variables.xyy = 1 x2
 9.5: In Exercises 36, solve using Separation of Variables.x dy dx y = 1 6
 9.6: In Exercises 36, solve using Separation of Variables.y = xy2 x2 + 1
 9.7: In Exercises 710, solve the Initial Value Separation of Variables. ...
 9.8: In Exercises 710, solve the Initial Value Separation of Variables.y...
 9.9: In Exercises 710, solve the Initial Value Separation of Variables.y...
 9.10: In Exercises 710, solve the Initial Value Separation of Variables.x...
 9.11: Figure 1 shows the slope field for dy dt = sin y + ty. Sketch the g...
 9.12: Sketch the slope field for dy dt = t 2y for 2 t 2, 2 y 2.
 9.13: Sketch the slope field for dy dt = y sin t for 2 t 2, 2 y 2.
 9.14: Which of the equations (i)(iii) corresponds to the slope field in F...
 9.15: Let y(t) be the solution to the differential equation with the slop...
 9.16: Let y(t) be the solution of 4 dy dt = y2 + t satisfying y(2) = 1. C...
 9.17: Let y(t) be the solution of (x3 + 1) dy dt = y satisfying y(0) = 1....
 9.18: In Exercises 1821, solve using the method of integrating factors. 1...
 9.19: In Exercises 1821, solve using the method of integrating factors dy...
 9.20: In Exercises 1821, solve using the method of integrating factors dy...
 9.21: In Exercises 1821, solve using the method of integrating factors y ...
 9.22: In Exercises 2229, solve using the appropriate method. 22. x2y = x2...
 9.23: In Exercises 2229, solve using the appropriate method.y + (tan x)y ...
 9.24: In Exercises 2229, solve using the appropriate method.xy = 2y + x 1...
 9.25: In Exercises 2229, solve using the appropriate method.(y 1)y = t, y...
 9.26: In Exercises 2229, solve using the appropriate method.y + 1 y = yte...
 9.27: In Exercises 2229, solve using the appropriate method.dw dx = k 1 +...
 9.28: In Exercises 2229, solve using the appropriate method.dw dx = k 1 +...
 9.29: In Exercises 2229, solve using the appropriate method.dw dx = k 1 +...
 9.30: Find the solutions to y = 4(y 12) satisfying y(0) = 20 and y(0) = 0...
 9.31: Find the solutions to y = 2y + 8 satisfying y(0) = 3 and y(0) = 4, ...
 9.32: Show that y = sin1 x satisfies the differential equation y = sec y ...
 9.33: What is the limit limt y(t) if y(t) is a solution of each of the fo...
 9.34: In Exercises 3437, let P (t) denote the balance at time t (years) o...
 9.35: In Exercises 3437, let P (t) denote the balance at time t (years) o...
 9.36: In Exercises 3437, let P (t) denote the balance at time t (years) o...
 9.37: In Exercises 3437, let P (t) denote the balance at time t (years) o...
 9.38: State whether the differential equation can be solved using Separat...
 9.39: Let A and B be constants. Prove that if A > 0, then all solutions o...
 9.40: At time t = 0, a tank of height 5 m in the shape of an inverted pyr...
 9.41: The trough in Figure 3 (dimensions in centimeters) is filled with w...
 9.42: Find the solution of the logistic equation dy dt = 0.4y(4 y) satisf...
 9.43: Let y(t) be the solution of dy dt = 0.3y(2 y) with y(0) = 1. Determ...
 9.44: Suppose that y = ky(1 y/8) has a solution satisfying y(0) = 12 and ...
 9.45: Alake has a carrying capacity of 1000 fish.Assume that the fish pop...
 9.46: A rabbit population on an island increases exponentially with growt...
 9.47: Show that y = sin(tan1 x + C) is the general solution of y = 1 y2/ ...
 9.48: A tank is filled with 300 liters (L) of contaminated water containi...
 9.49: At t = 0, a tank of volume 300 L is filled with 100 L of water cont...
 9.50: The outflow of the tank in Exercise 49 is directed into a second ta...
Solutions for Chapter 9: INTRODUCTION TO DIFFERENTIAL EQUATIONS
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 9: INTRODUCTION TO DIFFERENTIAL EQUATIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 9: INTRODUCTION TO DIFFERENTIAL EQUATIONS includes 50 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Since 50 problems in chapter 9: INTRODUCTION TO DIFFERENTIAL EQUATIONS have been answered, more than 44652 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3.

Argument of a complex number
The argument of a + bi is the direction angle of the vector {a,b}.

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Directed angle
See Polar coordinates.

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

Extracting square roots
A method for solving equations in the form x 2 = k.

Factored form
The left side of u(v + w) = uv + uw.

Finite series
Sum of a finite number of terms.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Inverse properties
a + 1a2 = 0, a # 1a

Inverse variation
See Power function.

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range

Onetoone rule of exponents
x = y if and only if bx = by.

Placebo
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Sample standard deviation
The standard deviation computed using only a sample of the entire population.

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Slopeintercept form (of a line)
y = mx + b