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
advanced engineering mathematics

Questions and Answers of Advanced Engineering Mathematics

Find a basis of solutions by the Frobenius method. Try to identify the series as expansions of known functions. Show the details of your work.(x + 2)2y" + (x + 2)y' - y = 0
Find a general solution in terms of Jv and Yv. Indicate whether you could also use J-v instead of Yv. Use the indicated substitution. Show the details of your work.xy" + 5y' + xy + 0 (y = u/x2)
Find the location and kind of all critical points of the given nonlinear system by linearization.y'1 = 2y2 + 2y22y'2 = -8y1
Find the location and kind of all critical points of the given nonlinear system by linearization.y'1 = cos y2y'2 = 3y1
Find the currents in Fig. 103 when R = 1 Î©, L = 1.25 H, C = 0.2 F, I1(0) = 1, I2(0) = 1 A. I2 L. Network in Problem 26 Fig. 103.
Tank T1in Fig. 101 initially contains 200 gal of water in which 160 lb of salt are dissolved. Tank T2initially contains 100 gal of pure water. Liquid is pumped through the system as indicated, and
Find a general solution. Show the details of your work.y'1 = y1 + y2 + sin ty'2 = 4y1 + y2
Find a general solution. Show the details of your work.y'1 = 2y1 + 2y2 + ety'2 = -2y1 - 3y2 + et
Each of the two tanks contains 200 gal of water, in which initially 100 lb (Tank T1) and 200 lb (Tank T2) of fertilizer are dissolved. The inflow, circulation, and outflow are shown in Fig. 88. The
What kind of critical point does y' = Ay have if A has the eigenvalues-4 and 2
Find the currents in Fig. 99 (Probs. 17€“19) for the following data, showing the details of your work.Solve Prob. 17 with E = 440 sin t V and the other data as before.Data from Prob. 17R1 =
(a) Set up the model for the (undamped) system in Fig. 81.(b) Solve the system of ODEs obtained. Try y = xeÏ‰t and set Ï‰2 = Î». Proceed as in Example 1 or 2.(c)
(a) Determine the type of the critical point at (0, 0) when Î¼ > 0, Î¼ = 0, Î¼ < 0.(b) Rayleigh equation. Show that the Rayleigh equation 0) " class="fr-fic fr-dib">also describes
Solve the following initial value problems.y'1 = -y1 - y2y'2 = y1 – y2y1(0) = 1, y2(0) = 0
Find a general solution. Determine the kind and stability of the critical point.y'1 = 3y1 + 4y2y'2 = 3y1 + 2y2
Solve, showing details:y'1 = 4y2 + 5ety'2 = -y1 - 20e-ty1(0) = 1, y2(0) = 0
Find a general solution of the given ODE (a) by first converting it to a system, (b), as given. Show the details of your work.y"' + 2y" - y' - 2y = 0
Solve y" + 1/9y = 0. Find the trajectories. Sketch or graph some of them.
Solve the following initial value problems.y'1 = y1 + 3y2y'2 = 1/3y 1 + y2y1(0) = 12, y2(0) = 2
Find a general solution. Determine the kind and stability of the critical point.y'1 = 5y1y'2 = y2
Solve, showing details:y'1 = y1 + 4y2 - t2 + 6ty'2 = y1 + y2 - t2 + t - 1y1(0) = 2, y2(0) = -1
Solve, showing details:y'1 = -3y1 - 4y2 + 5ety'2 = 5y1 + 6y2 - 6ety1(0) = 19, y2(0) = -23
Find a general solution of the given ODE (a) by first converting it to a system, (b), as given. Show the details of your work.y" + 3y' + 2y = 0
Find the location and type of all critical points by first converting the ODE to a system and then linearizing it.y" + y - y3 = 0
Determine the type and stability of the critical point. Then find a real general solution and sketch or graph some of the trajectories in the phase plane. Show the details of your work.y'1 = y2y'2 =
Solve the following initial value problems.y'1 = 2y1 + 2y2y'2 = 5y1 - y2y1(0) = 0, y2(0) = 7
In Example 2 find the currents:If the capacitance is changed to C = 5/27 F. (General solution only.)
Find the location and type of all critical points by linearization. Show the details of your work.y1' = y2 - y22y2' = y1 - y21
Determine the type and stability of the critical point. Then find a real general solution and sketch or graph some of the trajectories in the phase plane. Show the details of your work.y'1 = -y1 +
Find a real general solution of the following systems. Show the details.y'1 = 8y1 - y2y'2 = y1 + 10y2
Find a general solution. Show the details of your work.y'1 = 4y2y'2 = 4y1 - 16t2 + 2
Find the location and type of all critical points by linearization. Show the details of your work.y'1 = y2y2' = -y1 - y21
Determine the type and stability of the critical point. Then find a real general solution and sketch or graph some of the trajectories in the phase plane. Show the details of your work.y'1 = -6y1 -
Find a real general solution of the following systems. Show the details.y'1 = 2y1 - 2y2y'2 = 2y1 + 2y2
Find a general solution. Show the details of your work.y'1 = 4y1 - 8y2 + 2 cosh ty'2 = 2y1 - 6y2 + cosh t + 2 sinh t
Find the location and type of all critical points by linearization. Show the details of your work.y'1 = 4y1 - y21y'2 = y2
Determine the type and stability of the critical point. Then find a real general solution and sketch or graph some of the trajectories in the phase plane. Show the details of your work.y'1 = 2y1 +
Find a real general solution of the following systems. Show the details.y'1 = -8y1 - 2y2y'2 = 2y1 - 4y2
Find a general solution. Show the details of your work.y'1 = y1 + y2 + 10 cos ty'2 = 3y1 - y2 - 10 sin t
What happens in Example 1 if we replace T1 by a tank containing 200 gal of water and 150 lb of fertilizer dissolved in it?
Determine the type and stability of the critical point. Then find a real general solution and sketch or graph some of the trajectories in the phase plane. Show the details of your work.y'1 = -4y1y'2
Find a real general solution of the following systems. Show the details.y'1 = 6y1 + 9y2y'2 = y1 + 6y2
Prove that the product of two unitary n x n matrices and the inverse of a unitary matrix are unitary. Give examples.
Prove that eigenvectors of a symmetric matrix corresponding to different eigenvalues are orthogonal. Give examples.
Find an eigenbasis (a basis of eigenvectors) and diagonalize. Show the details. 1 0 -4
Find the eigenvalues. Find the corresponding eigenvectors. -3 1 -2 4 -1 -2 2 -2 3 2. 4)
Let A = [αjk] be an n x n matrix with (not necessarily distinct) eigenvalues λ1, · · · , λn. Show.The sum of the main diagonal entries, called the trace of A, equals the sum of the eigenvalues
Verify that A and AÌ‚ = p-1AP have the same spectrum. 19 4 2 12 1 P.
This important concept denotes a matrix that commutes with its conjugate transpose AA̅T = A̅TA. Prove that Hermitian, skew-Hermitian, and unitary matrices are normal. Give corresponding examples of
Do there exist non singular skew-symmetric n × n matrices with odd n?
Verify that A and AÌ‚ = p-1AP have the same spectrum. -4 -7 P =|0 3 1 1
Let A = [αjk] be an n x n matrix with (not necessarily distinct) eigenvalues λ1, · · · , λn. Show.kA has the eigenvalues kλ1,· · ·, kλn. Am(m = 1, 2, · · ·) has the eigenvalues λ1m, ·
Find an eigenbasis and diagonalize. 72 -56 - 56 513
Find the matrix A in the linear transformation y = Ax, where x = [x1 x2]T (x = [x1 x2 x3]T) are Cartesian coordinates. Find the eigenvalues and eigenvectors and
What kind of conic section (or pair of straight lines) is given by the quadratic form? Transform it to principal axes. Express xT = [x1 x2] in terms of the new coordinate
Do there exist nondiagonal symmetric 3 x 3 matrices that are orthogonal?
Find a simple matrix that is not normal. Find a normal matrix that is not Hermitian, skew-Hermitian, or unitary.
Transform to canonical form (to principal axes). Express [x1 x2]T in terms of the new variables [y1 y2]T..9x12 - 6x1x2 + 17x22 = 36
What kind of conic section (or pair of straight lines) is given by the quadratic form? Transform it to principal axes. Express xT = [x1 x2] in terms of the new coordinate
Transform to canonical form (to principal axes). Express [x1 x2]T in terms of the new variables [y1 y2]T.5x12 + 24x1x2 - 5x22 = 0
Show that A-1 exists if and only if the eigenvalues λ1, · · ·, λn are all nonzero, and then A-1 has the eigenvalues 1/λ1, · · ·,1/λn.
In Probs. 17€“19, using Kirchhoff€™s laws and showing the details, find the currents: 82 12 2 24 V 12 v
Showing the details, calculate the following expressions or give reason why they are not defined, when(A2)-1, (A-1)2 3 1 -3 4 1 2, B =-4 A = 4 -2 -3 2 V =-3
Showing all intermediate results, calculate the following expression or give reasons why they are undefined:ab, ba, aA, Bb Let 4 -2 3 -3 A =-2 1 B = -3 6. 1 2 2 -2 1. a = [1 -2 0], 0), b = 3 2 -2
By definition, forces are in equilibrium if their resultant is the zero vector. Find a force p such that the above u, v, w, and p are in equilibrium.
Same task as in Prob. 16 for the matrix in Prob. 7.Give an application of the matrix in Prob. 2 that makes the form of the inverse obvious.Data from Prob 2Find the inverse by Gauss€“Jordan
Are the following sets of vectors linearly independent? Show the details of your work. 14
Find the Euclidean norm of the vectors:[-4 8 -1]T
Showing all intermediate results, calculate the following expression or give reasons why they are undefined:bTAb, aBaT, aCCT, CTba Let 4 -2 3 -3 A =-2 1 B = -3 6. 1 2 2 -2 1. a = [1 -2 0], 0), b = 3
Matrices have various engineering applications, as we shall see. For instance, they can be used to characterize connections in electrical networks, in nets of roads, in production processes, etc., as
Are the following sets of vectors linearly independent? Show the details of your work. [1 2 3 4], [2 3 4 5], [3 4 5 6]. 4 5 6 7]
The idea is to get an equation from the vanishing of the determinant of a homogeneous linear system as the condition for a nontrivial solution in Cramer€™s theorem. We explain the trick for
Solve by Cramer’s rule. Check by Gauss elimination and back substitution. Show details.2x - 4y = -245x + 2y = 0
Determine the ranks of the coefficient matrix and the augmented matrix and state how many solutions the linear system will have.In Prob. 26Data from Prob. 26Showing the details, find all solutions or
Is the given set of vectors a vector space? Give reasons. If your answer is yes, determine the dimension and find a basis. (v1, v2, · · · denote components.)All vectors in R3 with 3v1 - 2v2 + v3 =
Find the currents. 220 V 10Ω (12 20 2 240 V
Are the given functions linearly independent or dependent on the half-axis x > 0? Give reason.cos2 x, sin2 x, 2π
Extend the method to Euler–Cauchy equations. Comment on the practical significance of such extensions.
Solve the following ODEs, showing the details of your work.y"' + 2y" - y' - 2y = 1 - 4x3
Solve the given ODE. Show the details of your work.yiv + 2y" + y = 0
Solve the following ODEs, showing the details of your work.(D3 + 3D2 - 5D – 39I)y = -300 cos x
Solve the given ODE. Show the details of your work.(D3 - D2 - D + l) y = 0
Solve the following ODEs, showing the details of your work.(D3 + 4D)y = sin x
Solve the given ODE. Show the details of your work.yiv - 3y" - 4y = 0
Solve the given ODE. Show the details of your work.(D5 + 8D3 + 16D)y = 0
Solve the given IVP, showing the details of your work.yiv - 5y" + 4y = l0e-3x, y(0) = 1, y' (0) = 0, y" (0) = 0, y"' (0) = 0
Are the given functions linearly independent or dependent on the half-axis x > 0? Give reason.x2, 1/x2, 0
Solve the given ODE. Show the details of your work.y"' - 4y" - y' + 4y = 30e2x
Solve the given IVP, showing the details of your work.x3y"' + xy' - y = x2, y(1) = 1, y' (1) = 3, y" (1) = 14
Are the given functions linearly independent or dependent on the half-axis x > 0? Give reason.e2x, xe2x, x2e2x
Solve the given ODE. Show the details of your work.x2y"' + 3xy" - 2y' = 0
Solve the given ODE. Show the details of your work.(D3 - D)y = sinh 0.8x
Are the given functions linearly independent or dependent on the half-axis x > 0? Give reason.sin2 x, cos2 x, cos 2x
Solve the given IVP, showing the details of your work.(D3 - 2D2 - 9D + 18I)y = e2x, y(0) = 4.5, y' (0) = 8.8, y" (0) = 17.2
Since variation of parameters is generally complicated, it seems worthwhile to try to extend the other method. Find out experimentally for what ODEs this is possible and for what not. Work backward,
Solve the given ODE. Show the details of your work.(D4 - 13D2 + 36I)y = 12ex
This is of practical interest since a single solution of an ODE can often be guessed.(a) How could you reduce the order of a linear constant-coefficient ODE if a solution is known?(b) Reduce x3y"' -
Solve the IVP. Show the details of your work.(D3 - D2 - D + I)y = 0, y(0) = 0, Dy(0) = 1, D2y(0) = 0
Solve the IVP. Show the details of your work.(D4 - 26D2 + 25I)y = 50(x + 1)2, y(0) = 12.16, Dy(0) = -6, D2y(0) = 34, D3y(0) = -130
Solve the IVP. Show the details of your work.(D3 + 3D2 + 3D + I)y = 8 sin x, y(0) = -1, y' (0) = -3, y" (0) = 5

Showing 3600 - 3700 of 3883

First
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

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