 9.5.1: 1 4 Determine whether the differential equation is linear.x y xy y
 9.5.2: 1 4 Determine whether the differential equation is linear.y xy 2 sxy
 9.5.3: 1 4 Determine whether the differential equation is linear.y 1x1y y
 9.5.4: 1 4 Determine whether the differential equation is linear.y sin x x...
 9.5.5: 514 Solve the differential equation.y y 1 y
 9.5.6: 514 Solve the differential equation.y y exy
 9.5.7: 514 Solve the differential equation.y x y 4x
 9.5.8: 514 Solve the differential equation.4x 3y x 4y sin3xx
 9.5.9: 514 Solve the differential equation.xy y sx y
 9.5.10: 514 Solve the differential equation.y y sinex11.
 9.5.11: 514 Solve the differential equation.sin x dydx cos xy sinx 2 x dy
 9.5.12: 514 Solve the differential equation.x dydx 4y x 4ex1
 9.5.13: 514 Solve the differential equation.1 t dudt u 1 t t 0t ln
 9.5.14: 514 Solve the differential equation.t ln tdrdt r tetx
 9.5.15: 1520 Solve the initialvalue problem.x 2y 2xy ln x y1 29.5
 9.5.16: 1520 Solve the initialvalue problem.t3 dydt 3t2y cos t y 0td
 9.5.17: 1520 Solve the initialvalue problem.tdudt t2 3u u2 42xy
 9.5.18: 1520 Solve the initialvalue problem.2xy y 6x x 0 y4 20xy
 9.5.19: 1520 Solve the initialvalue problem.xy y x 2 sin x y 0x 2
 9.5.20: 1520 Solve the initialvalue problem.x 2 1 dydx 3x y 1 0 y0 2Cxy 2y
 9.5.21: 2122 Solve the differential equation and use a graphing cal culator...
 9.5.22: 2122 Solve the differential equation and use a graphing cal culator...
 9.5.23: A Bernoulli differential equation (named after James Bernoulli) is ...
 9.5.24: 2425 Use the method of Exercise 23 to solve the differential equati...
 9.5.25: 2425 Use the method of Exercise 23 to solve the differential equati...
 9.5.26: Solve the secondorder equation by making the substitution
 9.5.27: In the circuit shown in Figure 4, a battery supplies a constant vol...
 9.5.28: In the circuit shown in Figure 4, a generator supplies a voltage of...
 9.5.29: The figure shows a circuit containing an electromotive force, a cap...
 9.5.30: In the circuit of Exercise 29, , , , and . Find the charge and the ...
 9.5.31: Let be the performance level of someone learning a skill as a funct...
 9.5.32: Two new workers were hired for an assembly line. Jim processed 25 u...
 9.5.33: In Section 9.3 we looked at mixing problems in which the volume of ...
 9.5.34: A tank with a capacity of 400 L is full of a mixture of water and c...
 9.5.35: An object with mass is dropped from rest and we assume that the air...
 9.5.36: . If we ignore air resistance, we can conclude that heavier objects...
 9.5.37: . (a) Show that the substitution transforms the logistic differenti...
 9.5.38: To account for seasonal variation in the logistic differential equa...
Solutions for Chapter 9.5: Linear Equations
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 9.5: Linear Equations
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Chapter 9.5: Linear Equations includes 38 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. Since 38 problems in chapter 9.5: Linear Equations have been answered, more than 31015 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Absolute value of a vector
See Magnitude of a vector.

Arccosecant function
See Inverse cosecant function.

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

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Dihedral angle
An angle formed by two intersecting planes,

Halfangle identity
Identity involving a trigonometric function of u/2.

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Horizontal component
See Component form of a vector.

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

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

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

Polar axis
See Polar coordinate system.

Principle of mathematical induction
A principle related to mathematical induction.

Quadric surface
The graph in three dimensions of a seconddegree equation in three variables.

Vertical asymptote
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a ƒ1x2 = q.

Vertices of an ellipse
The points where the ellipse intersects its focal axis.