All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question

Search
Sign In
Register

study help
mathematics
first course differential equations

Questions and Answers of First Course Differential Equations

Verify that if c is a constant, then the function defined piecewise bysatisfies the differential equation y' = -√1- y2 for all x. (Perhaps a preliminary sketch with c = 0 will be helpful.) Sketch a
Problems 30 through 32 explore the relation between the speed of an auto and the distance it skids when the brakes are applied.A car traveling at 60 mi/h (88 ft/s) skids 176 ft after its brakes are
Express the solution of the initial value problemas an integral as in Example 3 of this section. 2x- = y + 2x cos x, y(1) = 0 dy dx
Problems 29 through 32 explore the connections among general and singular solutions, existence, and uniqueness.(a) Find a general solution of the differential equation dy/dx = y2.(b) Find a singular
Problems 23 through 28 explore the motion of projectiles under constant acceleration or deceleration.A ball is thrown straight downward from the top of a tall building. The initial speed of the ball
Verify that if k is a constant, then the function y(x) ≡ kx satisfies the differential equation xy' = y for all x. Construct a slope field and several of these straight line solution curves. Then
In Problems 27 through 31, a function y = g(x) is described by some geometric property of its graph. Write a differential equation of the form dy/dx = f (x, y) having the function g as its solution
Verify that if c is a constant, then the function defined piecewise bysatisfies the differential equation y' = 3y2/3 for all x. Can you also use the "left half" of the cubic y = (x - c)3 in piecing
Express the general solution of dy/dx = 1 + 2xy in terms of the error function erf(x) = 2 元 e-1² dt.
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy 2√√x. dx cos² y, y(4) = π/4
Solve the differential equations in Problems 26 through 28 by regarding y as the independent variable rather than x. dy (1 + 2xy) = 1 + y² dx
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy dx 6e2x-y, y(0) = 0
The next seven problems illustrate the fact that, if the hypotheses of Theorem 1 are not satisfied, then the initial value problem y' = f (x,y), y(a) = b may have either no solutions, finitely many
In Problems 27 through 31, a function y = g(x) is described by some geometric property of its graph. Write a differential equation of the form dy/dx = f (x, y) having the function g as its solution
Solve the differential equations in Problems 26 through 28 by regarding y as the independent variable rather than x. (x + yey) dy = 1 dx
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy dx = 2xy²+3x²y²,y(1) = -1
Problems 23 through 28 explore the motion of projectiles under constant acceleration or deceleration.A projectile is fired straight upward with an initial velocity of 100 m=s from the top of a
Suppose the deer population P(t) in a small forest satisfies the logistic equationConstruct a slope field and appropriate solution curve to answer the following questions: If there are 25 deer at
Solve the differential equations in Problems 26 through 28 by regarding y as the independent variable rather than x. (1 - 4xy2) dy dx = y3
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy x=y=2x²y, y(1) = 1 dx
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy dx = y cotx, y ( 1 n ) = ½ n
Problems 23 through 28 explore the motion of projectiles under constant acceleration or deceleration.The brakes of a car are applied when it is moving at 100 km/h and provide a constant deceleration
Problems 23 through 28 explore the motion of projectiles under constant acceleration or deceleration.A ball is dropped from the top of a building 400 ft high. How long does it take to reach the
Problems 23 and 24 are like Problems 21 and 22, but now use a computer algebra system to plot and print out a slope field for the given differential equation. If you wish (and know how), you can
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy dx +1= 2y, y(1) = 1
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy dx = 4x³yy, y(1) = -3
Problems 23 and 24 are like Problems 21 and 22, but now use a computer algebra system to plot and print out a slope field for the given differential equation. If you wish (and know how), you can
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy 2y dx X √x²-16 2 y (5) = 2
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy dx = 3x² (y² + 1), y(0) = 1
In Problems 19 through 22, a particle starts at the origin and travels along the x-axis with the velocity function v(t) whose graph is shown in Figs. 1.2.6 through 1.2.9. Sketch the graph of the
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
In Problems 11 through 18, find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x (0), and initial velocity v0 = v(0).a(t) = 2t + 1, v0 = -7,
In Problems 11 through 18, find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x (0), and initial velocity v0 = v(0). a(t): = 1 (t+1)3 vo= 0,
Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy dx = yet, y(0) = 2e
In Problems 11 through 18, find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x (0), and initial velocity v0 = v(0).a(t) = 4(t + 3)2, v0 =
In Problems 11 through 18, find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x (0), and initial velocity v0 = v(0).a(t) = 50 sin 5t, v0 =
In Problems 11 through 18, find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x (0), and initial velocity v0 = v(0). I = 0x 'I =
Problems 54 through 64 illustrate the application of Torricelli’s law.A spherical tank of radius 4 ft is full of water when a circular bottom hole with radius 1 in. is opened. How long will be
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
A more detailed version of Theorem 1 says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f (x, y) exists on some open
In Problems 11 through 18, find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x (0), and initial velocity v0 = v(0).a(t) = 50, v0 = 10, x0 =
In Problems 11 through 18, find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x (0), and initial velocity v0 = v(0).a(t) = -20, v0 = -15, x0
In Problems 11 through 18, find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x (0), and initial velocity v0 = v(0).a(t) = 3t, v0 = 5, x0 = 0
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx = : xe *; y(0) = 1
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx || 1 1-x +2 (0) = 0
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx = cos 2x; y(0) = 1
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx 10 2 x + 1 -; y(0) = 0
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx -2 =xx +9; y(-4) = 0
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx la || 1 x + 2 ; (2) = -1
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx x ; y(1) = 5
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx || x; y (4) = 0
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx = (x - 2); y(2) = 1
In Problems 1 through 10, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional
In Problems 1 through 10, find a function y = f (x) satisfying the given differential equation and the prescribed initial condition. dy dx = 2x + 1; y(0) = 3
Just before midday the body of an apparent homicide victim is found in a room that is kept at a constant temperature of 70°F. At 12 noon the temperature of the body is 80°F and at 1 P.M. it is
A 12 h water clock is to be designed with the dimensions shown in Fig. 1.4.10, shaped like the surface obtained by revolving the curve y = f (x) around the y-axis. What should this curve be, and
A water tank has the shape obtained by revolving the parabola x2 = by around the y-axis. The water depth is 4 ft at 12 noon, when a circular plug in the bottom of the tank is removed. At 1 P.M. the
(a) Show that y(x) = Cx4 defines a one-parameter family of differentiable solutions of the differential equation xy' = 4y (Fig. 1.1.9).(b) Show thatdefines a differentiable solution of xy' = 4y for
In Example 7 we saw that y(x) = 1/(C - x) defines a one-parameter family of solutions of the differential equation dy/dx = y2.(a) Determine a value of C so that y (10) = 10.(b) Is there a value of C
Problems 45 and 46 deal with a shallow reservoir that has a one-square-kilometer water surface and an average water depth of 2 meters. Initially it is filled with fresh water, but at time t = 0 water
Problems 45 and 46 deal with a shallow reservoir that has a one-square-kilometer water surface and an average water depth of 2 meters. Initially it is filled with fresh water, but at time t = 0 water
Problems 43 through 46 concern the differential equationwhere k is a constant.(a) Assume that k is positive, and then sketch graphs of solutions of x' = kx2 with several typical positive values of
The barometric pressure p (in inches of mercury) at an altitude x miles above sea level satisfies the initial value problem dp/dx = (-0.2)p, p(0) = 29.92.(a) Calculate the barometric pressure at
The intensity I of light at a depth of x meters below the surface of a lake satisfies the differential equation dI/dx = (-1.4)I.(a) At what depth is the intensity half the intensity I0 at the surface
Figure 1.5.7 shows a slope field and typical solution curves for the equation y' = x - y.(a) Show that every solution curve approaches the straight line y = x - 1 as x → + ∞.(b) For each of the
Figure 1.5.8 shows a slope field and typical solution curves for the equation y' = x + y.(a) Show that every solution curve approaches the straight line y = - x - 1 as x → - ∞.(b) For each of the
A spacecraft is in free fall toward the surface of the moon at a speed of 1000 mph (mi/h). Its retrorockets, when fired, provide a constant deceleration of 20,000 mi/h2. At what height above the
When sugar is dissolved in water, the amount A that remains undissolved after t minutes satisfies the differential equation dA/dt = -kA (k > 0). If 25% of the sugar dissolves after 1 min, how long
A pitcher of buttermilk initially at 25°C is to be cooled by setting it on the front porch, where the temperature is 0°C. Suppose that the temperature of the buttermilk has dropped to 15°C after
In Problems 37 through 42, determine by inspection at least one solution of the given differential equation. That is, use your knowledge of derivatives to make an intelligent guess. Then test your
A certain moon rock was found to contain equal numbers of potassium and argon atoms. Assume that all the argon is the result of radioactive decay of potassium (its half-life is about 1.28 x 109
The amount A(t) of atmospheric pollutants in a certain mountain valley grows naturally and is tripling every 7.5 years.(a) If the initial amount is 10 pu (pollutant units), write a formula for A(t)
An accident at a nuclear power plant has left the surrounding area polluted with radioactive material that decays naturally. The initial amount of radioactive material present is 15 su (safe units),
According to one cosmological theory, when uranium was first generated in the early evolution of the universe following the “big bang,” the isotopes 235U and 238U were produced in equal amounts.
Problems 54 through 64 illustrate the application of Torricelli’s law.A tank is shaped like a vertical cylinder; it initially contains water to a depth of 9 ft, and a bottom plug is removed at time
In Problems 1 through 12, verify by substitution that each given function is a solution of the given differential equation.Throughout these problems, primes denote derivatives with respect to x.
Suppose a woman has enough “spring” in her legs to jump (on earth) from the ground to a height of 2.25 feet. If she jumps straight upward with the same initial velocity on the moon—where the
In Problems 37 through 42, determine by inspection at least one solution of the given differential equation. That is, use your knowledge of derivatives to make an intelligent guess. Then test your
At noon a car starts from rest at point A and proceeds at constant acceleration along a straight road toward point B. If the car reaches B at 12:50 P.M. with a velocity of 60 mi/h, what is the
Suppose that a = 0.5 mi, v0 = 9 mi/h, and vS = 3 mi/h as in Example 4, but that the velocity of the river is given by the fourth-degree function rather than the quadratic function in Eq. (18). Now
If a = 0.5 mi and v0 = 9 mi/h as in Example 4, what must the swimmer’s speed vS be in order that he drifts only 1 mile downstream as he crosses the river?Example 4 Example 4 River crossing Suppose
In Problems 37 through 42, determine by inspection at least one solution of the given differential equation. That is, use your knowledge of derivatives to make an intelligent guess. Then test your
At noon a car starts from rest at point A and proceeds with constant acceleration along a straight road toward point C, 35 miles away. If the constantly accelerated car arrives at C with a
Problems 43 through 46 concern the differential equationwhere k is a constant.(a) If k is a constant, show that a general (one-parameter) solution of the differential equation is given by x(t) = 1/(C
A driver involved in an accident claims he was going only 25 mph. When police tested his car, they found that when its brakes were applied at 25 mph, the car skidded only 45 feet before coming to a

Showing 1800 - 1900 of 2513

First
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Company Info

Security
Copyrights
Privacy Policy
Terms & Condition
SolutionInn Fee
Scholarship

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Copyright © 2024 SolutionInn All Rights Reserved.

Get the SolutionInn - Study Help App