 9.1.1: Determine the order of the following differential equations: (a) x5...
 9.1.2: Is y = sin x a linear differential equation? 3
 9.1.3: Give an example of a nonlinear differential equation of the form y ...
 9.1.4: Can a nonlinear differential equation be separable? If so, give an ...
 9.1.5: Give an example of a linear, nonseparable differential equation.
 9.1.6: In Exercises 38, verify that the given function is a solution of th...
 9.1.7: In Exercises 38, verify that the given function is a solution of th...
 9.1.8: In Exercises 38, verify that the given function is a solution of th...
 9.1.9: Which of the following equations are separable? Write those that ar...
 9.1.10: The following differential equations appear similar but have very d...
 9.1.11: The following differential equations appear similar but have very d...
 9.1.12: Consider the differential equation y3y 9x2 = 0. (a) Write it as y3 ...
 9.1.13: Verify that x2y + ey = 0 is separable. (a) Write it as ey dy = x2 d...
 9.1.14: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.15: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.16: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.17: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.18: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.19: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.20: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.21: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.22: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.23: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.24: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.25: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.26: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.27: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.28: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.29: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.30: In Exercises 1430, use Separation of Variables to find the general ...
 9.1.31: In Exercises 3144, solve the Initial Value Problem. 31. y + 2y = 0,...
 9.1.32: In Exercises 3144, solve the Initial Value Problem.y 3y + 12 = 0, y...
 9.1.33: In Exercises 3144, solve the Initial Value Problem.yy = xey2 , y(0)...
 9.1.34: In Exercises 3144, solve the Initial Value Problem.y2 dy dx = x3, y...
 9.1.35: In Exercises 3144, solve the Initial Value Problem.y = (x 1)(y 2), ...
 9.1.36: In Exercises 3144, solve the Initial Value Problem.y = (x 1)(y 2), ...
 9.1.37: In Exercises 3144, solve the Initial Value Problem.y = x(y2 + 1), y...
 9.1.38: In Exercises 3144, solve the Initial Value Problem.(1 t) dy dt y = ...
 9.1.39: In Exercises 3144, solve the Initial Value Problem.dy dt = yet , y(...
 9.1.40: In Exercises 3144, solve the Initial Value Problem.dy dt = tey, y(1...
 9.1.41: In Exercises 3144, solve the Initial Value Problem.t 2 dy dt t = 1 ...
 9.1.42: In Exercises 3144, solve the Initial Value Problem.1 x2 y = y2 + 1,...
 9.1.43: In Exercises 3144, solve the Initial Value Problem.y = tan y, y(ln ...
 9.1.44: In Exercises 3144, solve the Initial Value Problem.y = y2 sin x, y(...
 9.1.45: Find all values of a such that y = xa is a solution of y 12x2y = 0 46
 9.1.46: Find all values of a such that y = eax is a solution of y + 4y 12y ...
 9.1.47: In Exercises 47 and 48, let y(t) be a solution of (cos y + 1) dy dt...
 9.1.48: Assuming that y(6) = /3, find an equation of the tangent line to th...
 9.1.49: In Exercises 4954, use Eq. (4) and Torricellis Law [Eq. (5)]. Water...
 9.1.50: In Exercises 4954, use Eq. (4) and Torricellis Law [Eq. (5)]. At t ...
 9.1.51: In Exercises 4954, use Eq. (4) and Torricellis Law [Eq. (5)]. The t...
 9.1.52: In Exercises 4954, use Eq. (4) and Torricellis Law [Eq. (5)]. A tan...
 9.1.53: In Exercises 4954, use Eq. (4) and Torricellis Law [Eq. (5)]. Atank...
 9.1.54: In Exercises 4954, use Eq. (4) and Torricellis Law [Eq. (5)]. A cyl...
 9.1.55: Figure 8 shows a circuit consisting of a resistor of R ohms, a capa...
 9.1.56: Assume in the circuit of Figure 8 that R = 200 ohms, C = 0.02 farad...
 9.1.57: According to one hypothesis, the growth rate dV /dt of a cells volu...
 9.1.58: We might also guess that the volume V of a melting snowball decreas...
 9.1.59: In general, (fg) is not equal to f g , but let f (x) = e3x and find...
 9.1.60: A boy standing at point B on a dock holds a rope of length attached...
 9.1.61: Show that the differential equations y = 3y/x and y = x/3y define o...
 9.1.62: Find the family of curves satisfying y = x/y and sketch several mem...
 9.1.63: A 50kg model rocket lifts off by expelling fuel downward at a rate...
 9.1.64: Let v(t) be the velocity of an object of mass m in freefall near t...
 9.1.65: If a bucket of water spins about a vertical axis with constant angu...
 9.1.66: In Section 6.2, we computed the volume V of a solid as the integral...
 9.1.67: A basic theorem states that a linear differential equation of order...
 9.1.68: Show that y = Cerx is a solution of y + ay + by = 0 if and only if ...
 9.1.69: A spherical tank of radius R is halffilled with water. Suppose tha...
Solutions for Chapter 9.1: Solving Differential Equations
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 9.1: Solving Differential Equations
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Chapter 9.1: Solving Differential Equations includes 69 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 69 problems in chapter 9.1: Solving Differential Equations have been answered, more than 40796 students have viewed full stepbystep solutions from this chapter.

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

Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

Constant
A letter or symbol that stands for a specific number,

Elimination method
A method of solving a system of linear equations

Expanded form
The right side of u(v + w) = uv + uw.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

First octant
The points (x, y, z) in space with x > 0 y > 0, and z > 0.

Geometric series
A series whose terms form a geometric sequence.

Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

Implied domain
The domain of a function’s algebraic expression.

Logistic regression
A procedure for fitting a logistic curve to a set of data

Odd function
A function whose graph is symmetric about the origin (ƒ(x) = ƒ(x) for all x in the domain of f).

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Scatter plot
A plot of all the ordered pairs of a twovariable data set on a coordinate plane.

Sequence
See Finite sequence, Infinite sequence.

Slant line
A line that is neither horizontal nor vertical

Sum identity
An identity involving a trigonometric function of u + v

Trigonometric form of a complex number
r(cos ? + i sin ?)

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.

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