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# Solutions for Chapter 1.2: Initial-Value Problems

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

ISBN: 9780495108368

Solutions for Chapter 1.2: Initial-Value Problems

Solutions for Chapter 1.2
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##### ISBN: 9780495108368

Chapter 1.2: Initial-Value Problems includes 45 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Differential Equations with Boundary-Value Problems was written by and is associated to the ISBN: 9780495108368. Since 45 problems in chapter 1.2: Initial-Value Problems have been answered, more than 15541 students have viewed full step-by-step solutions from this chapter. 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
• Additive inverse of a real number

The opposite of b , or -b

• Causation

A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

• Components of a vector

See Component form of a vector.

• Confounding variable

A third variable that affects either of two variables being studied, making inferences about causation unreliable

• Exponential growth function

Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

• Extracting square roots

A method for solving equations in the form x 2 = k.

• Hyperboloid of revolution

A surface generated by rotating a hyperbola about its transverse axis, p. 607.

• Initial value of a function

ƒ 0.

• Inverse cotangent function

The function y = cot-1 x

• Linear regression line

The line for which the sum of the squares of the residuals is the smallest possible

• Midpoint (on a number line)

For the line segment with endpoints a and b, a + b2

• Order of magnitude (of n)

log n.

• Parametric curve

The graph of parametric equations.

• Permutations of n objects taken r at a time

There are nPr = n!1n - r2! such permutations

• Pie chart

See Circle graph.

• Response variable

A variable that is affected by an explanatory variable.

• Rigid transformation

A transformation that leaves the basic shape of a graph unchanged.

• Solve a triangle

To find one or more unknown sides or angles of a triangle

• Variance

The square of the standard deviation.

• Vertical translation

A shift of a graph up or down.

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