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# Solutions for Chapter 2.5: Solutions by Substitutions

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

ISBN: 9780495108368

Solutions for Chapter 2.5: Solutions by Substitutions

Solutions for Chapter 2.5
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##### ISBN: 9780495108368

Chapter 2.5: Solutions by Substitutions includes 38 full step-by-step solutions. Differential Equations with Boundary-Value Problems was written by and is associated to the ISBN: 9780495108368. This textbook survival guide was created for the textbook: Differential Equations with Boundary-Value Problems, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Since 38 problems in chapter 2.5: Solutions by Substitutions have been answered, more than 15427 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Categorical variable

In statistics, a nonnumerical variable such as gender or hair color. Numerical variables like zip codes, in which the numbers have no quantitative significance, are also considered to be categorical.

• Conjugate axis of a hyperbola

The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

• Coordinate plane

See Cartesian coordinate system.

• Determinant

A number that is associated with a square matrix

• 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

• Equivalent equations (inequalities)

Equations (inequalities) that have the same solutions.

• First quartile

See Quartile.

• Gaussian elimination

A method of solving a system of n linear equations in n unknowns.

• Hyperbola

A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

• Infinite discontinuity at x = a

limx:a + x a ƒ(x) = q6 or limx:a - ƒ(x) = q.

• Main diagonal

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

• Minor axis

The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

• Multiplication property of equality

If u = v and w = z, then uw = vz

• Multiplicative inverse of a complex number

The reciprocal of a + bi, or 1 a + bi = a a2 + b2- ba2 + b2 i

• Perpendicular lines

Two lines that are at right angles to each other

• PH

The measure of acidity

• Polynomial function

A function in which ƒ(x)is a polynomial in x, p. 158.

• Polynomial interpolation

The process of fitting a polynomial of degree n to (n + 1) points.

• Quotient polynomial

See Division algorithm for polynomials.

• Rose curve

A graph of a polar equation or r = a cos nu.

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