Solutions for FIRST CRSE.IN DIFF.EQUAT..-ACCESS
Problem 1E:
Under the same assumptions that underlie the model in (1), determine a differential equation for the...Problem 2E:
The population model given in (1) fails to take death into consideration; the growth rate equals the...Problem 3E:
Using the concept of net rate introduced in Problem 2, determine a model for a population P(t) if...Problem 4E:
Modify the model in Problem 3 for net rate at which the population P(t) of a certain kind of fish...Problem 5E:
A cup of coffee cools according to Newtons law of cooling (3). Use data from the graph of the...Problem 6E:
The ambient temperature Tm in (3) could be a function of time t. Suppose that in an artificially...Problem 7E:
Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students....Problem 8E:
At a time denoted as t = 0 a technological innovation is introduced into a community that has a...Problem 9E:
Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt...Problem 10E:
Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt...Problem 11E:
What is the differential equation in Problem 10, if the well-stirred solution is pumped out at a...Problem 12E:
Generalize the model given in equation (8) of this section by assuming that the large tank initially...Problem 13E:
Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water...Problem 14E:
The right-circular conical tank shown in Figure 1.3.13 loses water out of a circular hole at its...Problem 15E:
A series circuit contains a resistor and an inductor as shown in Figure 1.3.14. Determine a...Problem 16E:
A series circuit contains a resistor and a capacitor as shown in Figure 1.3.15. Determine a...Problem 17E:
For high-speed motion through the airsuch as the skydiver shown in Figure 1.3.16, falling before the...Problem 18E:
A cylindrical barrel s feet in diameter of weight w lb is floating in water as shown in Figure...Problem 19E:
After a mass m is attached to a spring, it stretches it s units and then hangs at rest in the...Problem 20E:
In Problem 19, what is a differential equation for the displacement x(t) if the motion takes place...Problem 21E:
A small single-stage rocket is launched vertically as shown in Figure 1.3.19. Once launched, the...Problem 22E:
In Problem 21, the mass m(t) is the sum of three different masses: m(t) = mp + mv + mf(t), where mp...Problem 23E:
By Newtons universal law of gravitation the free-fall acceleration a of a body, such as the...Problem 24E:
Suppose a hole is drilled through the center of the Earth and a bowling ball of mass m is dropped...Problem 25E:
Learning Theory In the theory of learning, the rate at which a subject is memorized is assumed to be...Problem 26E:
Forgetfulness In Problem 25 assume that the rate at which material is forgotten is proportional to...Problem 27E:
Infusion of a Drug A drug is infused into a patients bloodstream at a constant rate of r grams per...Problem 28E:
Tractrix A motorboat starts at the origin and moves in the direction of the positive x-axis, pulling...Problem 29E:
Reflecting surface Assume that when the plane curve C shown in Figure 1.3.23 is revolved about the...Problem 30E:
Reread Problem 45 in Exercises 1.1 and then give an explicit solution P(t) for equation (1). Find a...Problem 34E:
Rotating Fluid As shown in Figure 1.3.24(a), a right-circular cylinder partially filled with fluid...Problem 37E:
Let It snow The snowplow problem is a classic and appears in many differential equations texts, but...Problem 38E:
Population Dynamics Suppose that dP/dt = 0.15 P(t) represents a mathematical model for the growth of...Browse All Chapters of This Textbook
Chapter 1 - Introduction To Differential EquationsChapter 1.1 - Definitions And TerminologyChapter 1.2 - Initial-value ProblemsChapter 1.3 - Differential Equations As Mathematical ModelsChapter 2 - First-order Differential EquationsChapter 2.1 - Solution Curves Without A SolutionChapter 2.2 - Separable EquationsChapter 2.3 - Linear EquationsChapter 2.4 - Exact EquationsChapter 2.5 - Solutions By Substitutions
Chapter 2.6 - A Numerical MethodChapter 3 - Modeling With First-order Differential EquationsChapter 3.1 - Linear ModelsChapter 3.2 - Nonlinear ModelsChapter 3.3 - Modeling With Systems Of First-order DesChapter 4 - Higher-order Differential EquationsChapter 4.1 - Preliminary Theory-linear EquationsChapter 4.2 - Reduction Of OrderChapter 4.3 - Homogeneous Linear Equations With Constant CoefficientsChapter 4.4 - Undetermined Coefficients-superposition ApproachChapter 4.5 - Undetermined Coefficients-annihilator ApproachChapter 4.6 - Variation Of ParametersChapter 4.7 - Cauchy-euler EquationsChapter 4.8 - Green's FunctionsChapter 4.9 - Solving Systems Of Linear Des By EliminationChapter 4.10 - Nonlinear Differential EquationsChapter 5 - Modeling With Higher-order Differential EquationsChapter 5.1 - Linear Models: Initial-value ProblemsChapter 5.2 - Linear Models: Boundary-value ProblemsChapter 5.3 - Nonlinear ModelsChapter 6 - Series Solutions Of Linear EquationsChapter 6.1 - Review Of Power SeriesChapter 6.2 - Solutions About Ordinary PointsChapter 6.3 - Solutions About Singular PointsChapter 6.4 - Special FunctionsChapter 7 - The Laplace TransformChapter 7.1 - Definition Of The Laplace TransformChapter 7.2 - Inverse Transforms And Transforms Of DerivativesChapter 7.3 - Operational Properties IChapter 7.4 - Operational Properties IiChapter 7.5 - The Dirac Delta FunctionChapter 7.6 - Systems Of Linear Differential EquationsChapter 8 - Systems Of Linear First-order Differential EquationsChapter 8.1 - Preliminary Theory-linear SystemsChapter 8.2 - Homogeneous Linear SystemsChapter 8.3 - Nonhomogeneous Linear SystemsChapter 8.4 - Matrix ExponentialChapter 9 - Numerical Solutions Of Ordinary Differential EquationsChapter 9.1 - Euler Methods And Error AnalysisChapter 9.2 - Runge-kutta MethodsChapter 9.3 - Multistep MethodsChapter 9.4 - Higher-order Equations And SystemsChapter 9.5 - Second-order Boundary-value ProblemsChapter A - Integral-defined FunctionsChapter B - Matrices
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