 9.2.1E: Use the RK4 method with h = 0.1 to approximate y(0.5), where y(x) i...
 9.2.2E: Assume that in (4). Use the resulting secondorder RungeKutta metho...
 9.2.3E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.4E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.5E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.6E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.7E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.8E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.9E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.10E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.11E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.12E: In 3–12 use the RK4 method with h = 0.1 to obtain a fourdecimal ap...
 9.2.13E: If air resistance is proportional to the square of the instantaneou...
 9.2.14E: A mathematical model for the area A (in cm2) that a colony of bacte...
 9.2.15E: Consider the initialvalue problem See in Exercises 9.1.(a) Compare...
 9.2.16E: Consider the initialvalue problem The analytic solution is y(x) = ...
 9.2.17E: Repeat using the initialvalue problem Reference : Consider the ini...
 9.2.18E: Consider the initialvalue problem y(1) = 5. The analytic solution ...
 9.2.19E: Repeat for the initialvalue problem y(0) = 0. The analytic solutio...
 9.2.20E: A count of the number of evaluations of the function f used in solv...
 9.2.21E: The RK4 method for solving an initialvalue problem over an interva...
Solutions for Chapter 9.2: A First Course in Differential Equations with Modeling Applications 10th Edition
Full solutions for A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
Solutions for Chapter 9.2
Get Full SolutionsChapter 9.2 includes 21 full stepbystep solutions. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. This expansive textbook survival guide covers the following chapters and their solutions. Since 21 problems in chapter 9.2 have been answered, more than 48555 students have viewed full stepbystep solutions from this chapter. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052.

Additive inverse of a real number
The opposite of b , or b

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

Inverse cosecant function
The function y = csc1 x

Odd function
A function whose graph is symmetric about the origin (ƒ(x) = ƒ(x) for all x in the domain of f).

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Root of a number
See Principal nth root.

Semimajor axis
The distance from the center to a vertex of an ellipse.

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

Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

Third quartile
See Quartile.

Trigonometric form of a complex number
r(cos ? + i sin ?)

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.