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# Solutions for Chapter 5.1: Linear Models: Initial-Value Problems

## Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition

ISBN: 9780495108368

Solutions for Chapter 5.1: Linear Models: Initial-Value Problems

Solutions for Chapter 5.1
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##### ISBN: 9780495108368

Since 58 problems in chapter 5.1: Linear Models: Initial-Value Problems have been answered, more than 15540 students have viewed full step-by-step solutions from this chapter. Differential Equations with Boundary-Value Problems was written by and is associated to the ISBN: 9780495108368. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.1: Linear Models: Initial-Value Problems includes 58 full step-by-step solutions. This textbook survival guide was created for the textbook: Differential Equations with Boundary-Value Problems, edition: 7.

Key Calculus Terms and definitions covered in this textbook
• Arctangent function

See Inverse tangent function.

• Commutative properties

a + b = b + a ab = ba

• Component form of a vector

If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x-, y-, and z-components of the vector, respectively)

• Direct variation

See Power function.

• Directrix of a parabola, ellipse, or hyperbola

A line used to determine the conic

• Discriminant

For the equation ax 2 + bx + c, the expression b2 - 4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2 - 4AC

• Division

a b = aa 1 b b, b Z 0

• Implied domain

The domain of a function’s algebraic expression.

• Initial value of a function

ƒ 0.

• Linear regression equation

Equation of a linear regression line

• Local extremum

A local maximum or a local minimum

• Local maximum

A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

• nth root of unity

A complex number v such that vn = 1

• Parametrization

A set of parametric equations for a curve.

• Probability of an event in a finite sample space of equally likely outcomes

The number of outcomes in the event divided by the number of outcomes in the sample space.

• Root of an equation

A solution.

• 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.

• Sinusoidal regression

A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

• Sum of functions

(ƒ + g)(x) = ƒ(x) + g(x)

• Xscl

The scale of the tick marks on the x-axis in a viewing window.

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