 1.2.1: In 1 and 2, y 1(1 c1ex ) is a oneparameter family of solutions of ...
 1.2.2: In 1 and 2, y 1(1 c1ex ) is a oneparameter family of solutions of ...
 1.2.3: In 36, y 1(x2 c) is a oneparameter family of solutions of the firs...
 1.2.4: In 36, y 1(x2 c) is a oneparameter family of solutions of the firs...
 1.2.5: In 36, y 1(x2 c) is a oneparameter family of solutions of the firs...
 1.2.6: In 36, y 1(x2 c) is a oneparameter family of solutions of the firs...
 1.2.7: In 710, x c1 cos t c2 sin t is a twoparameter family of solutions ...
 1.2.8: In 710, x c1 cos t c2 sin t is a twoparameter family of solutions ...
 1.2.9: In 710, x c1 cos t c2 sin t is a twoparameter family of solutions ...
 1.2.10: In 710, x c1 cos t c2 sin t is a twoparameter family of solutions ...
 1.2.11: In 1114, y c1ex c2ex is a twoparameter family of solutions of the ...
 1.2.12: In 1114, y c1ex c2ex is a twoparameter family of solutions of the ...
 1.2.13: In 1114, y c1ex c2ex is a twoparameter family of solutions of the ...
 1.2.14: In 1114, y c1ex c2ex is a twoparameter family of solutions of the ...
 1.2.15: In 15 and 16 determine by inspection at least two solutions of the ...
 1.2.16: In 15 and 16 determine by inspection at least two solutions of the ...
 1.2.17: In 1724 determine a region of the xyplane for which the given diff...
 1.2.18: In 1724 determine a region of the xyplane for which the given diff...
 1.2.19: In 1724 determine a region of the xyplane for which the given diff...
 1.2.20: In 1724 determine a region of the xyplane for which the given diff...
 1.2.21: In 1724 determine a region of the xyplane for which the given diff...
 1.2.22: In 1724 determine a region of the xyplane for which the given diff...
 1.2.23: In 1724 determine a region of the xyplane for which the given diff...
 1.2.24: In 1724 determine a region of the xyplane for which the given diff...
 1.2.25: In 2528 determine whether Theorem 1.2.1 guarantees that the differe...
 1.2.26: In 2528 determine whether Theorem 1.2.1 guarantees that the differe...
 1.2.27: In 2528 determine whether Theorem 1.2.1 guarantees that the differe...
 1.2.28: In 2528 determine whether Theorem 1.2.1 guarantees that the differe...
 1.2.29: (a) By inspection find a oneparameter family of solutions of the d...
 1.2.30: (a) Verify that y tan (x c) is a oneparameter family of solutions ...
 1.2.31: (a) Verify that y 1(x c) is a oneparameter family of solutions of ...
 1.2.32: (a) Show that a solution from the family in part (a) of that satisf...
 1.2.33: (a) Verify that 3x2 y2 c is a oneparameter family of solutions of ...
 1.2.34: (a) Use the family of solutions in part (a) of to find an implicit ...
 1.2.35: In 3538 the graph of a member of a family of solutions of a second...
 1.2.36: In 3538 the graph of a member of a family of solutions of a second...
 1.2.37: In 3538 the graph of a member of a family of solutions of a second...
 1.2.38: In 3538 the graph of a member of a family of solutions of a second...
 1.2.39: In 39 and 40 use in Exercises 1.1 and (2) and (3) of this section.
 1.2.40: In 39 and 40 use in Exercises 1.1 and (2) and (3) of this section.
 1.2.41: Consider the initialvalue problem y x 2y, . Determine which of the...
 1.2.42: Determine a plausible value of x0 for which the graph of the soluti...
 1.2.43: Suppose that the firstorder differential equation dydx f(x, y) pos...
 1.2.44: The functions and have the same domain but are clearly different. S...
 1.2.45: Population Growth Beginning in the next section we will see that di...
Solutions for Chapter 1.2: InitialValue Problems
Full solutions for Differential Equations with BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 1.2: InitialValue Problems
Get Full SolutionsChapter 1.2: InitialValue Problems includes 45 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368. Since 45 problems in chapter 1.2: InitialValue Problems have been answered, more than 15541 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems, edition: 7.

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 = cot1 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.