 6.2.1E: In 1–14, find a general solution for the differential equation with...
 6.2.2E: In 1–14, find a general solution for the differential equation with...
 6.2.3E: In 1–14, find a general solution for the differential equation with...
 6.2.4E: In 1–14, find a general solution for the differential equation with...
 6.2.5E: In 1–14, find a general solution for the differential equation with...
 6.2.6E: In 1–14, find a general solution for the differential equation with...
 6.2.7E: In 1–14, find a general solution for the differential equation with...
 6.2.8E: In 1–14, find a general solution for the differential equation with...
 6.2.9E: In 1–14, find a general solution for the differential equation with...
 6.2.10E: In 1–14, find a general solution for the differential equation with...
 6.2.11E: In 1–14, find a general solution for the differential equation with...
 6.2.12E: In 1–14, find a general solution for the differential equation with...
 6.2.13E: In 1–14, find a general solution for the differential equation with...
 6.2.14E: In 1–14, find a general solution for the differential equation with...
 6.2.15E: In 15–18, find a general solution to the given homogeneous equation.
 6.2.16E: In 15–18, find a general solution to the given homogeneous equation.
 6.2.17E: In 15–18, find a general solution to the given homogeneous equation.
 6.2.18E: In 15–18, find a general solution to the given homogeneous equation.
 6.2.19E: In 19–21, solve the given initial value problem.
 6.2.20E: In 19–21, solve the given initial value problem.
 6.2.21E: In 19–21, solve the given initial value problem.
 6.2.22E: In 22 and 23, find a general solution for the given linear system u...
 6.2.23E: In 22 and 23, find a general solution for the given linear system u...
 6.2.24E: Let be a polynomial with real coefficients an, . . . , a0. Prove th...
 6.2.25E: Show that the m functions are linearly independent on [Hint: Show t...
 6.2.26E: As an alternative proof that the functions er1x,er2x, . . . , ernx ...
 6.2.27E: Find a general solution to by using Newton’s method (Appendix B) or...
 6.2.28E: Find a general solution to by using Newton’s method or some other n...
 6.2.29E: Find a general solution to by using Newton’s method to approximate ...
 6.2.30E: (a) Derive the form for the general solution to the equation from t...
 6.2.31E: HigherOrder Cauchy–Euler Equations. A differential equation that c...
 6.2.32E: Let y(x) = Cerx, where C and r are real numbers, be a solution to a...
 6.2.33E: On a smooth horizontal surface, a mass of m1 kg is attached to a fi...
 6.2.34E: Suppose the two springs in the coupled mass–spring system discussed...
 6.2.35E: Vibrating Beam. In studying the transverse vibrations of a beam, on...
Solutions for Chapter 6.2: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 6.2
Get Full SolutionsSince 35 problems in chapter 6.2 have been answered, more than 37363 students have viewed full stepbystep solutions from this chapter. Chapter 6.2 includes 35 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730.

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Exponential form
An equation written with exponents instead of logarithms.

Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.

Frequency distribution
See Frequency table.

Graphical model
A visible representation of a numerical or algebraic model.

Identity properties
a + 0 = a, a ? 1 = a

Inverse cosecant function
The function y = csc1 x

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Inverse tangent function
The function y = tan1 x

Leastsquares line
See Linear regression line.

Maximum rvalue
The value of r at the point on the graph of a polar equation that has the maximum distance from the pole

Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Slope
Ratio change in y/change in x

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

Vertical stretch or shrink
See Stretch, Shrink.

xaxis
Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.