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

In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of
In Problems 7 through 12, use the Wronskian to prove that the given functions are linearly independent on the indicated interval.f(x) = 1 , g(x) = x , h(x) = x2 ; the real line
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y'' - 4y = sinh x
The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping
Find the general solutions of the differential equations in Problems 1 through 20.y'' - 6y' + 13y = 0
In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of
Each of Problems 15 through 18 gives the parameters for a forced mass-spring-dashpot system with equation mx" + cx' + kx = F0 cos ωt. Investigate the possibility of practical resonance of this
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y(5) + 5y(4) - y = 17
Find the general solutions of the differential equations in Problems 1 through 20.y(4) + 18y" + 81y = 0
In Problems 13 through 20, a third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions. y(3) -5y"
The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y" + 9y = 2x2e3x + 5
Each of Problems 15 through 18 gives the parameters for a forced mass-spring-dashpot system with equation mx" + cx' + kx = F0 cos ωt. Investigate the possibility of practical resonance of this
In Problems 13 through 20, a third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions. y(3) +9y'
Find the general solutions of the differential equations in Problems 1 through 20.6y(4) + 11y" + 4y = 0
The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y" + y = sinx + x cos x
Each of Problems 15 through 18 gives the parameters for a forced mass-spring-dashpot system with equation mx" + cx' + kx = F0 cos ωt. Investigate the possibility of practical resonance of this
The following three problems illustrate the fact that the superposition principle does not generally hold for nonlinear equations.Show that y = 1/x is a solution of y' + y2 = 0, but that if c ≠ 0
In Problems 13 through 20, a third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions. y(3)-3y"
The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping
Find the general solutions of the differential equations in Problems 1 through 20.y(4) = 16y
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y(4) - 5y'' + 4y = ex - xe2x
Find the general solutions of the differential equations in Problems 1 through 20.y(3) + y'' - y' - y = 0
The following three problems illustrate the fact that the superposition principle does not generally hold for nonlinear equations.Show that y = x3 is a solution of yy'' = 6x4, but that if c2 ≠ 1,
The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping
A mass weighing 100 lb (mass m = 3.125 slugs in fps units) is attached to the end of a spring that is stretched 1 in. by a force of 100 lb. A force F0 cos ωt acts on the mass. At what frequency (in
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y(5) + 2y(3) + 2y" = 3x2 - 1
The following three problems illustrate the fact that the superposition principle does not generally hold for nonlinear equations.Show that y1 ≡ and y2 = √x are solutions of yy'' + (y')2 = 0, but
Find the general solutions of the differential equations in Problems 1 through 20.y(4) + 2y(3) + 3y" + 2y' + y = 0
In Problems 13 through 20, a third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions. x³y (3) +
A front-loading washing machine is mounted on a thick rubber pad that acts like a spring; the weight W = mg (with g = 9.8 m/s2) of the machine depresses the pad exactly 0.5 cm. When its rotor spins
The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y(3) - y = ex + 7
In Problems 21 through 30, set up the appropriate form of a particular solution yp, but do not determine the values of the coefficients.y'' - 2y' + 2y = ex sin x
Determine whether the pairs of functions in Problems 20 through 26 are linearly independent or linearly dependent on the real line.f(x) = π, g(x) = cos2x + sin2x
Figure 5.6.10 shows a mass m on the end of a pendulum (of length L) also attached to a horizontal spring (with constant k). Assume small oscillations of m so that the spring remains essentially
In Problems 21 through 24, a nonhomogeneous differential equation, a complementary solution yc , and a particular solution yp are given. Find a solution satisfying the given initial
The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping
Solve the initial value problems given in Problems 21 through 26.y" - 4y' + 3y = 0; y(0) = 7, y' (0) = 11
In Problems 21 through 30, set up the appropriate form of a particular solution yp, but do not determine the values of the coefficients.y(5) - y(3) = ex + 2x2 - 5
Determine whether the pairs of functions in Problems 20 through 26 are linearly independent or linearly dependent on the real line.f(x) = x3, g(x) = x2|x|
Solve the initial value problems given in Problems 21 through 26.9y" + 6y' + 4y = 0; y(0) = 3, y' (0) = 4
A mass m hangs on the end of a cord around a pulley of radius a and moment of inertia I, as shown in Fig. 5.6.11. The rim of the pulley is attached to a spring (with constant k). Assume small
In Problems 21 through 24, a nonhomogeneous differential equation, a complementary solution yc , and a particular solution yp are given. Find a solution satisfying the given initial conditions.y" -
In Problems 21 through 30, set up the appropriate form of a particular solution yp, but do not determine the values of the coefficients.y" + 4y = 3x cos 2x
Determine whether the pairs of functions in Problems 20 through 26 are linearly independent or linearly dependent on the real line.f(x) = 1 + x, g(x) = 1 + |x|
In Problems 21 through 24, a nonhomogeneous differential equation, a complementary solution yc , and a particular solution yp are given. Find a solution satisfying the given initial conditions.y" -
A building consists of two floors. The first floor is attached rigidly to the ground, and the second floor is of mass m = 1000 slugs (fps units) and weighs 16 tons (32,000 lb). The elastic frame of
Determine whether the pairs of functions in Problems 20 through 26 are linearly independent or linearly dependent on the real line.f(x) = xex, g(x) = |x|ex
In Problems 21 through 30, set up the appropriate form of a particular solution yp, but do not determine the values of the coefficients.y(3) - y" - 12y' = x - 2xe-3x
Find the acute angles (in degrees) of each of the right triangles of Problems 5–8, respectively.In Problems 5–8, the three vertices A, B, and C of a triangle are given. Prove that each triangle
In Problems 9–16, express the indicated vector w as a linear combination of the given vectors v1, v2, ....., vk if this is possible. If not, show that it is impossible.w = (1, 0, 0,-1); v1 = (7,-6,
In Problems 9–16, express the indicated vector w as a linear combination of the given vectors v1, v2, ....., vk if this is possible. If not, show that it is impossible.w = (3,-1,-2); v1 = (-3, 1,
In Problems 9–16, express the indicated vector w as a linear combination of the given vectors v1, v2, ....., vk if this is possible. If not, show that it is impossible.w = (1,0,-7); v1 = (5,3,4),
Use Laplace transforms to solve the initial value problems in Problems 1 through 16.x'' + 4x = 0; x(0) = 5, x' (0) = 0
Use Laplace transforms to solve the initial value problems in Problems 1 through 16.x" + 9x = 0; x (0) = 3, x' (0) = 4
Find the convolution f(t) * g(t) in Problems 1 through 6.f(t) = t, g(t) = eat
Apply the definition in (1) to find directly the Laplace transforms of the functions described (by formula or graph) in Problems 1 through 10.f(t) = t2
Apply the translation theorem to find the Laplace transforms of the functions in Problems 1 through 4. f(t) = 13/2e-4t
Use Laplace transforms to solve the initial value problems in Problems 1 through 16.x" - x' - 2x = 0; x (0) = 0, x' (0) = 2
Find the inverse Laplace transform f (t) of each function given in Problems 1 through 10. Then sketch the graph of f. F(s) = e -S -38 e $2
Find the convolution f(t) * g(t) in Problems 1 through 6.f(t) = g(t) = sin t
Apply the definition in (1) to find directly the Laplace transforms of the functions described (by formula or graph) in Problems 1 through 10.f(t) = e3t + 1
Find the inverse Laplace transform f (t) of each function given in Problems 1 through 10. Then sketch the graph of f. F(s) = -S s+2
Apply the translation theorem to find the Laplace transforms of the functions in Problems 1 through 4. f(t) = e-2¹ sin 3πt
Find the inverse Laplace transform f (t) of each function given in Problems 1 through 10. Then sketch the graph of f. F(s) = e-se2-2s s-1
Apply the definition in (1) to find directly the Laplace transforms of the functions described (by formula or graph) in Problems 1 through 10.f(t) = cost
Find the convolution f(t) * g(t) in Problems 1 through 6.f(t) = t2, g(t) = cost
Use Laplace transforms to solve the initial value problems in Problems 1 through 16.x" + 8x' + 15x = 0; x (0) = 2, x'(0) = -3
Use Laplace transforms to solve the initial value problems in Problems 1 through 16.x" + x = sin 2t; x (0) = 0 = x' (0)
In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of
In Problems 7 through 12, use the Wronskian to prove that the given functions are linearly independent on the indicated interval.f(x) = ex , g(x) = e2x , h(x) = e3x ; the real line
In Problems 5 through 8, assume that the differential equation of a simple pendulum of length L is Lθ'' + gθ = 0, where g = GM/R2 is the gravitational acceleration at the location of the pendulum
In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of
Find the general solutions of the differential equations in Problems 1 through 20.y'' + 8y' + 25y = 0
In each of Problems 7 through 10, find the steady periodic solution xsp(t) = C cos(ωt - α) of the given equation mx" + cx' + kx = F(t) with periodic forcing function F(t) of frequency ω. Then
In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of
In each of Problems 7 through 10, find the steady periodic solution xsp(t) = C cos(ωt - α) of the given equation mx" + cx' + kx = F(t) with periodic forcing function F(t) of frequency ω. Then
Consider a floating cylindrical buoy with radius r, height h, and uniform density ρ ≦ 0.5 (recall that the density of water is 1 g/cm3). The buoy is initially suspended at rest with its bottom at
Find the general solutions of the differential equations in Problems 1 through 20.5y(4) + 3y(3) = 0
In Problems 7 through 12, use the Wronskian to prove that the given functions are linearly independent on the indicated interval.f(x) = ex , g(x) = x-2, h(x) = x-2 In x ; x > 0
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y" + 9y = 2 cos 3x + 3 sin 3x
In each of Problems 11 through 14, find and plot both the steady periodic solution xsp(t) = C cos(ωt - α) of the given differential equation and the actual solution x(t) = xsp(t) + Xtr(t) that
Find the general solutions of the differential equations in Problems 1 through 20.y(4) - 8y(3) + 16y" = 0
In Problems 7 through 12, use the Wronskian to prove that the given functions are linearly independent on the indicated interval.f(x) = x , g(x) = xex , h(x) = x2ex ; the real line
In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y(3) + 4y' = 3x - 1
In each of Problems 11 through 14, find and plot both the steady periodic solution xsp(t) = C cos(ωt - α) of the given differential equation and the actual solution x(t) = xsp(t) + Xtr(t) that
Find the general solutions of the differential equations in Problems 1 through 20.y(4) - 3y(3) + 3y" - y' = 0
Assume that the earth is a solid sphere of uniform density, with mass M and radius R = 3960 (mi). For a particle of mass m within the earth at distance r from the center of the earth, the
In Problems 7 through 12, use the Wronskian to prove that the given functions are linearly independent on the indicated interval.f(x) = x , g(x) = cos(lnx) , h(x) = sin(In x) ; x > 0
In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y(3) + y' = 2 - sin x
In each of Problems 11 through 14, find and plot both the steady periodic solution xsp(t) = C cos(ωt - α) of the given differential equation and the actual solution x(t) = xsp(t) + Xtr(t) that
Find the general solutions of the differential equations in Problems 1 through 20.9y(3) + 12y" + 4y' = 0
In each of Problems 7 through 10, find the steady periodic solution xsp(t) = C cos(ωt - α) of the given equation mx" + cx' + kx = F(t) with periodic forcing function F(t) of frequency ω. Then
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y" - 4y = cosh 2x
In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x.y" + 2y' - 3y = 1 + xex
Apply the translation theorem to find the inverse Laplace transforms of the functions in Problems 5 through 10. F(s) = 3 2S-4

Showing 700 - 800 of 2513

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last

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