 2.5.1: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.2: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.3: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.4: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.5: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.6: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.7: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.8: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.9: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.10: Each DE in 114 is homogeneous. In 110 solve the given differential ...
 2.5.11: Each DE in 114 is homogeneous. In 1114 solve the given initialvalu...
 2.5.12: Each DE in 114 is homogeneous. In 1114 solve the given initialvalu...
 2.5.13: Each DE in 114 is homogeneous. In 1114 solve the given initialvalu...
 2.5.14: Each DE in 114 is homogeneous. In 1114 solve the given initialvalu...
 2.5.15: Each DE in 1522 is a Bernoulli equation. In 1520 solve the given di...
 2.5.16: Each DE in 1522 is a Bernoulli equation. In 1520 solve the given di...
 2.5.17: Each DE in 1522 is a Bernoulli equation. In 1520 solve the given di...
 2.5.18: Each DE in 1522 is a Bernoulli equation. In 1520 solve the given di...
 2.5.19: Each DE in 1522 is a Bernoulli equation. In 1520 solve the given di...
 2.5.20: Each DE in 1522 is a Bernoulli equation. In 1520 solve the given di...
 2.5.21: Each DE in 1522 is a Bernoulli equation. In 21 and 22 solve the giv...
 2.5.22: Each DE in 1522 is a Bernoulli equation. In 21 and 22 solve the giv...
 2.5.23: Each DE in 2330 is of the form given in (5). In 2328 solve the give...
 2.5.24: Each DE in 2330 is of the form given in (5). In 2328 solve the give...
 2.5.25: Each DE in 2330 is of the form given in (5). In 2328 solve the give...
 2.5.26: Each DE in 2330 is of the form given in (5). In 2328 solve the give...
 2.5.27: Each DE in 2330 is of the form given in (5). In 2328 solve the give...
 2.5.28: Each DE in 2330 is of the form given in (5). In 2328 solve the give...
 2.5.29: Each DE in 2330 is of the form given in (5). In 29 and 30 solve the...
 2.5.30: Each DE in 2330 is of the form given in (5). In 29 and 30 solve the...
 2.5.31: Explain why it is always possible to express any homogeneous differ...
 2.5.32: Put the homogeneous differential equation (5x2 2y2 ) dx xy dy 0 int...
 2.5.33: (a) Determine two singular solutions of the DE in 10. (b) If the in...
 2.5.34: In Example 3 the solution y(x) becomes unbounded as x : . Neverthel...
 2.5.35: The differential equation dydx P(x) Q(x)y R(x)y2 is known as Riccat...
 2.5.36: Determine an appropriate substitution to solve xy y ln(xy).
 2.5.37: Falling Chain In in Exercises 2.4 we saw that a mathematical model ...
 2.5.38: Population Growth In the study of population dynamics one of the mo...
Solutions for Chapter 2.5: Solutions by Substitutions
Full solutions for Differential Equations with BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 2.5: Solutions by Substitutions
Get Full SolutionsChapter 2.5: Solutions by Substitutions includes 38 full stepbystep solutions. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368. This textbook survival guide was created for the textbook: Differential Equations with BoundaryValue 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 stepbystep solutions from this chapter.

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.