 11.1.1: Is y = x3 a solution to the differential equation xy 3y = 0?
 11.1.2: Determine whether each function is a solution to the differential e...
 11.1.3: Determine whether each function is a solution to the differential e...
 11.1.4: Show that y(x) = Aex is a solution to the equation y = y for any va...
 11.1.5: Show that y = sin 2t satisfies d2y dt2 + 4y = 0.
 11.1.6: Show that, for any constant P0, the function P = P0et satisfies the...
 11.1.7: Use implicit differentiation to show that x2 + y2 = r2 is a solutio...
 11.1.8: A quantity Q satisfies the differential equation dQ dt = t Q 0.5. (...
 11.1.9: Fill in the missing values in the table given if you know that dy/d...
 11.1.10: Use the method that generated the data in Table 11.1 on page 587 to...
 11.1.11: In Exercises 1114, find the particular solution to the differential...
 11.1.12: In Exercises 1114, find the particular solution to the differential...
 11.1.13: In Exercises 1114, find the particular solution to the differential...
 11.1.14: In Exercises 1114, find the particular solution to the differential...
 11.1.15: Show that y = A + Cekt is a solution to the equation dy dt = k(y A).
 11.1.16: Find the value(s) of for which y = cos t satisfies d2y dt2 + 9y = 0.
 11.1.17: Show that any function of the form x = C1 cosh t + C2 sinh t satisf...
 11.1.18: Suppose Q = Cekt satisfies the differential equation dQ dt = 0.03Q....
 11.1.19: Find the values of k for which y = x2 + k is a solution to the diff...
 11.1.20: For what values of k (if any) does y =5+3ekx satisfy the differenti...
 11.1.21: (a) For what values of C and n (if any) is y = Cxn a solution to th...
 11.1.22: (a) Find the value of A so that the equation y xyx = 0 has a soluti...
 11.1.23: In Figure 11.3, the height, y, of the hanging cable above the horiz...
 11.1.24: Match solutions and differential equations. (Note: Each equation ma...
 11.1.25: Pick out which functions are solutions to which differential equati...
 11.1.26: Families of curves often arise as solutions of differential equatio...
 11.1.27: Is y(x) = e3x the general solution of y = 3y?
 11.1.28: (a) Let y = A + Be2t . For what values of A and B, if any, is y a s...
 11.1.29: Q = 6e4t is the general solution to the differential equation dQ/dt...
 11.1.30: If dx/dt = 1/x and x = 3 when t = 0, then x is a decreasing functio...
 11.1.31: A differential equation with an initial condition.
 11.1.32: A secondorder differential equation
 11.1.33: A differential equation and two different solutions to the differen...
 11.1.34: A differential equation that has a trigonometric function as a solu...
 11.1.35: A differential equation that has a logarithmic function as a solution.
 11.1.36: A differential equation all of whose solutions are increasing and c...
 11.1.37: A differential equation all of whose solutions have their critical ...
 11.1.38: If y = f(t) is a particular solution to a firstorder differential ...
 11.1.39: Polynomials are never solutions to differential equations
 11.1.40: In 4047, is the statement true or false? Assume that y = f(x) is a ...
 11.1.41: In 4047, is the statement true or false? Assume that y = f(x) is a ...
 11.1.42: In 4047, is the statement true or false? Assume that y = f(x) is a ...
 11.1.43: In 4047, is the statement true or false? Assume that y = f(x) is a ...
 11.1.44: In 4047, is the statement true or false? Assume that y = f(x) is a ...
 11.1.45: In 4047, is the statement true or false? Assume that y = f(x) is a ...
 11.1.46: In 4047, is the statement true or false? Assume that y = f(x) is a ...
 11.1.47: In 4047, is the statement true or false? Assume that y = f(x) is a ...
Solutions for Chapter 11.1: WHAT IS A DIFFERENTIAL EQUATION?
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter 11.1: WHAT IS A DIFFERENTIAL EQUATION?
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.1: WHAT IS A DIFFERENTIAL EQUATION? includes 47 full stepbystep solutions. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. Since 47 problems in chapter 11.1: WHAT IS A DIFFERENTIAL EQUATION? have been answered, more than 35093 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

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

Combination
An arrangement of elements of a set, in which order is not important

Continuous function
A function that is continuous on its entire domain

Distance (on a number line)
The distance between real numbers a and b, or a  b

Index of summation
See Summation notation.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

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

Modulus
See Absolute value of a complex number.

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

nth root of unity
A complex number v such that vn = 1

Origin
The number zero on a number line, or the point where the x and yaxes cross in the Cartesian coordinate system, or the point where the x, y, and zaxes cross in Cartesian threedimensional space

Perihelion
The closest point to the Sun in a planet’s orbit.

Pole
See Polar coordinate system.

Reflection across the yaxis
x, y and (x,y) are reflections of each other across the yaxis.

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Secant
The function y = sec x.

Spiral of Archimedes
The graph of the polar curve.

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.

Xmax
The xvalue of the right side of the viewing window,.