1) Find the weighting, potential and stiffness functions in: H" –2 xH'+32H =0 where 2 is eigenvalue.

Q: H.W.: prove that the eigenfunctions ,(x) =cos x) and ,(x) =cos x) cOs are orthogonal.

A: Given eigenfunctions are ψ1x=1acosπ2ax and ψ2x=9acosπ2ax We need to prove that eigenfunctions ψ1x…

Q: Find the eigenvalues and eigenfunction of the following Saturm-Liouville equation y + Ay = 0 with…

A:

Q: The eigenfunctions for y"- 2y' + Xy = 0, y(0) = 1, y(1) = 0 are o {c* sin(nrx)} 1 o {e sin(")}-1 100…

A: First condition should be y(0)=0, from the given answer there is no option such that y(0)=1.

Q: Let Ae Mu (R) with A%+3A = -21. Show that if: I eigenvalue of A > » A-1 Va --2.

A:

Q: Given the Sturm-Liouville problem. -X"(x) = AX(x), x E (0, L), X (0) - aX(0) = 0, X'(L) + bX(L) = 0,…

A:

Q: 1. Consider the eigenvalue problem " (x) + [A – a²]ø(r) = 0, with O (0) = 0, and o'(1) = 0. Show…

A:

Q: Use the eigenfunction solution of the regular Sturm-Liouville problem: dx +ây = 0, y'(0) = y(1) = 0…

A:

Q: Given the problem Utt = Urx + uz; 0 0 u(0, t) = 0 = u(T, t) Show that this results in a…

A: utt=uxx+un   0<x<π, t>0u(0,t)=0=u(πt)Let u(nt) is a solution of typeu(nt)=x(n)T(t)where…

Q: If x=cos n= cos 2 TIX, are the eigenfunctions for the following IBVP u, =U+cos( x); + cos 0<x<1…

A: This question is about application of boundary value problem

Q: Determine the eigen values and eigen factors of the following Hormagencous integral equation u 6) =…

A:

Q: Show that the following SL problem has a negative eigenvalue y"(x) + Ay(x) = 0, y'(0) = 0, y(1) –…

A:

Q: (2 1 Q2) find eigenvalue eigenvector of A x(0,0) = (1,1)

A:

Q: Example 1. Prove that the homogeneous integral equation o(x) =À (3x - 2) to(t) dt %3D has no…

A: Solution

Q: The eigenvalues for y" + Ay= 0, y(0) = 0; y'(27) = 0 are (2n-1)2 16 n=1 { n² 1F In=0 n² 1° O 16 In=0…

A:

Q: 4. Consider the following boundary value problem for y(x) on 1(-2, 2]: (*) y" + 6y + dy = 0, y(-2) =…

A:

Q: Let A be a Then x (t) = e equations: x' (t) = Az(t). True False eigenvalue of A with a corresponding…

A: Given: For the matrix A, λ is the eigen value with the corresponding eigen vector v. The objective…

Q: 13. Consider the eigenvalue problem y"+ 2y' + Ay = 0; y(0) = y(1) = 0. %3D (a) Show that A = 1 is…

A:

Q: 12. Consider the eigenvalue problem y" + ìy = 0; y(-n)= y(1), y'(-x) = y'(1), which is not of the…

A: Given y"+λy=0, y-π=yπ and y'-π=y'π a) If λ=0, then  y"=0y(x)=Ax+B where A,B,C are any constantsAs…

Q: Prove that the Y,o spherical harmonic is an eigenfunction of the A2 (Legendrian) operator by…

A: As per the question we have to prove that the spherical harmonic function Y1,0 is a eigenfunction of…

Q: Consider the Sturm-Liouville Problem x²?y" – 3xy + 4Xy = 0, (1) = 0 y(3) = 0 %3D (a) Find all…

A: “Since you have asked multiple questions, we will solve the first question for you i.e. (a). If you…

Q: 5. The Hamiltonian for an axially symmetric rotator is L;+ L; L 21, 213 (a) What are the eigenvalues…

A: Solution is in next step

Q: The eigenfunctions for y"-2y + Ay = 0, y(0) = 1, y(1) = 0 are O {e I sin ()}, n-1 O {e² sin(")},…

A:

Q: Prove that the eigenvalue problem  y''+ (lamba)y=0,     y(0)=0,       y(1)+y'(1)=0  has no negative…

A:

Q: и — 100и,ди — 0, 0 0, - u(0, t) = 0, u(1, t) = 0, t> 0, u (х, 0) — sin(2mа) — sin (5та), 0<T<1.

A:

Q: Find all solution to the eigenvalue problem -X" =XX. X(-L) = X (L) & X'(−L) = X ' (L)

A: The given problem is to find the all solutions for the given eigen value problem with given boundary…

Q: Find the Eigenvalues and Eigenfunctions of the following Sturm_Liouville problems posed. y´´ + λy=0…

A:

Q: = Show that the following SL problem has a negative eigenvalue y"(x) + Ay(x) = 0, y'(0) = 0, (y(1) –…

A:

Q: Find the smallest Eigen value approximately using Rayleigh Ritz method y' + Ay = 0, y(0)=y(1)=0

A:

Q: Sy" + Ay = 0 r € (0, 1) y (0) = y (1) = 0.

A:

Q: The second approximation of the eigenvalue obtained by the power method applied to 0 -2 A=2 -1 1…

A:

Q: 9. Two coupled quantities, displacement s and velocity v, are related through the system: ds dt dv =…

A:

Q: Investigate whether the F(x)=e*² function is an eigenvalue function of the operator. If the…

A: Given: The function Fx=e-x22 and A^=d2dx2-x2 operator.

Q: (a) Suppose that T : R° → R° has a 5-dimensional eigenspace for the eigenvalue 1. Then show that…

A:

Q: The eigenfunctions for y"- 2y'+ Xy = 0, y(0) = 1, y(1) = 0 are o {c² sin(nrx)} 1 00 O {e sin(")}n-1…

A: We consider y(0)=0, from the given answer there is no option such that y(0)=1.

Q: 7. |Suppose A has det(A) = 2, eigenvalues A1 = 5, A2 = -1 and 1 eigenvectors vị = () () -3…

A:

Q: Find all positive eigenvalues and eigen functions for the Sturm-Liouville y" + xy = 0, y'(0) = 0, t…

A: .....

Q: dY 4 Y %3D dt -1

A:

Q: 1. Find the eigen values and eigen functions of the homogeneous integral equation y(x) = A /. (4x?t…

A: Given: The eigenvalues and eigenfunctions are determined for the homogeneous integral equation as…

Q: (iii) Let A c R" be symmetric and à an eigenvalue of 4. J2| is a singular value of A.

A: Given that A is a symmetric matrix and λ be an eigen value of A. That is, There exists a non zero…

Q: (a) The eigenfunctions of the following eigenvalue problem: X" + XX=0, X(0)= X(x)=0 are given by…

A:

Q: 9. Sketch the phase portrait and classify (by stating whether the origin is a stable or unstable…

A: (9A) Given the DE is dx→dt=Ax→ where the eigenvalues and eigenvectors of A are defined as: v1=21,…

Q: determine eigenvalues and eigenvectors if the eigenvalues are real. Also, determine the general…

A: dxdt=xdydt=x-3ydxdt=xdxx=dtintegrate it logx=t+ax=et+a=betdydt=bet-3ydydt+3y=betthis is linear…

Q: 1. Determine the eigenvalues and corresponding eigenfunctions of the boundary value problem as…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the following differential system: 2 1(0) with -3 y(0). Hint. One eigenvalue and its…

A: Consider the equation as shown below: Here,xy = -12-1-3xy with x0y0 = 4-2 And the object is to find…

Q: 2. Use the product method and solve an eigenvalue problem to find the solution of the following…

A: We will solve by the method of PDE

Q: 2. Consider the eigenvalue problem, y" + ày = 0, for 0 < x < 1/2; y' (0) = 0, y(n/2) = 0. Find all…

A: Given differential equation is y'' + λy = 0 with y'(0) = 0, y(π/2) = 0

Q: In ethod of eigenfunction expansions he methC 15. y(0) 0, y(1)-0

A: Given differential equation is y" = -x , y(0)=0 &amp; y(1)=0

Q: Consider the problem of heat flow in a uniform wire of length 2 described by 0 0, 4 Əx²' du du (2,…

A:

Q: Show that the function = xex is an eigenfunction of the operator d² Ô dx² where a is a constant.…

A: Given the function ϕ=xeax and operator O^=d2dx2-2ax