- 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 initial-value problem.x 2y 2xy ln x y1 29.5
- 9.5.16: 1520 Solve the initial-value problem.t3 dydt 3t2y cos t y 0td
- 9.5.17: 1520 Solve the initial-value problem.tdudt t2 3u u2 42xy
- 9.5.18: 1520 Solve the initial-value problem.2xy y 6x x 0 y4 20xy
- 9.5.19: 1520 Solve the initial-value problem.xy y x 2 sin x y 0x 2
- 9.5.20: 1520 Solve the initial-value 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 second-order 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
Absolute value of a vector
See Magnitude of a vector.
See Inverse cosecant function.
The notation PQ denoting the directed line segment with initial point P and terminal point Q.
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 three-dimensional space
An angle formed by two intersecting planes,
Identity involving a trigonometric function of u/2.
The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.
See Component form of a vector.
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.
Point where a curve crosses the x-, y-, or z-axis in a graph.
Inverse composition rule
The composition of a one-toone 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 + ae-kx, 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
A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).
See Polar coordinate system.
Principle of mathematical induction
A principle related to mathematical induction.
The graph in three dimensions of a seconddegree equation in three variables.
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.