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# Solutions for Chapter 2.5: SOLUTIONS BY SUBSTITUTIONS ## Full solutions for A First Course in Differential Equations with Modeling Applications | 10th Edition

ISBN: 9781111827052 Solutions for Chapter 2.5: SOLUTIONS BY SUBSTITUTIONS

Solutions for Chapter 2.5
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##### ISBN: 9781111827052

This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.5: SOLUTIONS BY SUBSTITUTIONS includes 38 full step-by-step solutions. Since 38 problems in chapter 2.5: SOLUTIONS BY SUBSTITUTIONS have been answered, more than 50121 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Arc length formula

The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

• Coefficient of determination

The number r2 or R2 that measures how well a regression curve fits the data

• Conic section (or conic)

A curve obtained by intersecting a double-napped right circular cone with a plane

• Demand curve

p = g(x), where x represents demand and p represents price

• Directed distance

See Polar coordinates.

• Frequency distribution

See Frequency table.

• Future value of an annuity

The net amount of money returned from an annuity.

• Graph of an equation in x and y

The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

• Independent variable

Variable representing the domain value of a function (usually x).

• Interquartile range

The difference between the third quartile and the first quartile.

• Inverse sine function

The function y = sin-1 x

• 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

• Main diagonal

The diagonal from the top left to the bottom right of a square matrix

• Natural logarithmic function

The inverse of the exponential function y = ex, denoted by y = ln x.

• Positive numbers

Real numbers shown to the right of the origin on a number line.

• Range screen

See Viewing window.

• Rational numbers

Numbers that can be written as a/b, where a and b are integers, and b ? 0.

• Richter scale

A logarithmic scale used in measuring the intensity of an earthquake.

• Vector equation for a line in space

The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

• Vertices of an ellipse

The points where the ellipse intersects its focal axis.