 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 o...
 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 3944, is a twoparameter family of solutions of the secondorder ...
 1.2.40: In 3944, is a twoparameter family of solutions of the secondorder ...
 1.2.41: In 3944, is a twoparameter family of solutions of the secondorder ...
 1.2.42: In 3944, is a twoparameter family of solutions of the secondorder ...
 1.2.43: In 3944, is a twoparameter family of solutions of the secondorder ...
 1.2.44: In 3944, is a twoparameter family of solutions of the secondorder ...
 1.2.45: Find a function y f(x) whose graph at each point (x, y) has the slo...
 1.2.46: Find a function y f(x) whose second derivative is y 12x 2 at each p...
 1.2.47: Consider the initialvalue problem y x 2y, . Determine which of the...
 1.2.48: Determine a plausible value of x0 for which the graph of the soluti...
 1.2.49: Suppose that the firstorder differential equation dydx f(x, y) pos...
 1.2.50: The functions and have the same domain but are clearly different. S...
 1.2.51: Beginning in the next section we will see that differential equatio...
Solutions for Chapter 1.2: INITIALVALUE PROBLEMS
Full solutions for A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
Solutions for Chapter 1.2: INITIALVALUE PROBLEMS
Get Full SolutionsA First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. Chapter 1.2: INITIALVALUE PROBLEMS includes 51 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Since 51 problems in chapter 1.2: INITIALVALUE PROBLEMS have been answered, more than 49902 students have viewed full stepbystep solutions from this chapter.

Acceleration due to gravity
g ? 32 ft/sec2 ? 9.8 m/sec

Average velocity
The change in position divided by the change in time.

Base
See Exponential function, Logarithmic function, nth power of a.

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Constraints
See Linear programming problem.

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

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

Frequency distribution
See Frequency table.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Identity function
The function ƒ(x) = x.

Inverse cotangent function
The function y = cot1 x

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

xzplane
The points x, 0, z in Cartesian space.