Question 2 (Repeated Eigenvalues x' 1 Solve 15 x(0) 5+2t x(t = 2 +t - e3t +2e2t – 12t – 7] 2e3t – 2e2t + 6t +5 71 x(t): x(t) = 42 5lat 2.

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A: The eigen values λn and the eigen functions yn of the Strum-Liouville problem: y''+9λy=0,…

Q: Please solve the following by hand, use a step by step approach and explain each step as you go with…

A: Step 1:Step 2:Step 3:Step 4:Step 5:Step 6:

Q: What is eigenvalues and eigenvectors for the following system of ODES? x' = 5x1 +3x2 x'2 = -x + x2…

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Q: Let vk = Yk () Consider the difference equation vk+1 = Avk with initial condition vo = where A is a…

A: Consider the given difference equation.

Q: Find all the Eigen-values and Eigen-functions for the following BVP. y" + ly = 0 with y(-n) = y(n) ,…

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Q: e1+e2+e3+e4+e5+e6 = 16 where ei >= 0. What is the generating function? and what is the coefficient…

A: The given equation is e1+e2+e3+e4+e5+e6=16, where ei≥0. Since ei≥0, therefore the generating…

Q: (x'(1) Exercises: 1- Solve 3 Yx(1) 2 y(1))

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

Q: 30. E=2*10^5 I=30000 L=600 W=25 y = dy dx = W 120EIL 3 (-x ² + 21³x² - (^x) W 120EIL (-5X² +…

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Q: 5. Consider the ordinary differential equation Orx + Ao = 0 (a) Determine the eigenvalues An and…

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Q: Consider the following matrix ^-18 11]. A = (a) Find the eigenvalues and the eigenvectors of this…

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Q: y" + Ay = 0, y(-2) = y(2), 3/(-2) = y'(2) %3D

A: Given         y''+ λy = 0,        y -2=y2,     y'(-2)=y'2 ........(1)

Q: Suppose the size of a population evolves according to the logistic equa- tion: dN = 1.5N dt N 100…

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Q: The eigenvalues for y" + Ay = 0, y(0) = 0; y'(#) = 0 are

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Q: Let x (t) = = x"(t) x' (t) If x (0) 21(t) = = = x₂(t) = sin( 9 [] -11 -21 Put the eigenvalues in…

A: Rewrite the system of first order differential equations.

Q: Suppose A E L(R") has a real eigenvalue \ < 0. Then the equation x' = = Ax

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Q: The nth root of a number can be approximated by the recursive formula 1 A = ((n-1) R₁+ n (R₁)¹- R…

A: Given Data: The nth root of a number can be approximated by the recursive formula,…

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: d the eigenvalues and eigenfunctions for the following boundary value proble y" + Xy = 0 with y'(0)…

A: Given the equation y''+λy=0 with y'0=0, y'2=0. Consider the auxiliary equation,  r2+λ=0r=±λi…

Q: A circle C in the plane x+y+z= -1 has a radius of 3 and center (2,0, - 3). Evaluate F.dr for F =…

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Q: E=2*10^5 I=30000 L=600 W=25 y = dy dx W 120EIL = 120 FIL (-5X² + 6(³X²-1²) ū assume as р 38, P = =…

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Q: Please solve the follwoing question by hand. Be deatiled and please explain each step as you go so…

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Q: 27. (Critical point) What kind of critical point does y' = Ay have if A has the eigenvalues -6 and…

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Q: Please solve the following by hand, have good detail and explain each part of the question step by…

A: image was blurr but i have tried my best to solve.

Q: 2 2 -6 8. The general solution of x' = x is: (Hint: 6 is an eigenvalue.) 2 -1 -3 -2 - 1 -2 3 1 (a) x…

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Q: u = 2 uzz) 0 0 with boundary/initial conditions: u(0, t) = 0, u(6, t) = 0, S 2, 0<z<3 1 0, 3 < a < 6…

A: Given that,  ut=2uxx,  0&lt;x&lt;6,  t≥0⋯⋯(1) BC: Ux(0,t)=0, ux6,t=0 IC: ux,0=2,  0&lt;x≤30,…

Q: 0 _º(¹)_dt=1+x+x² solve the integral equation √x-t

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A: To find the eigenvalues and eigenfunctions for the differential equation:y'' - 2y' + (1 + lambda)y =…

Q: Solve the IVP 22 + 1ox+1 %3D y Co) =0, y'(0) = -6 Osi ng the quasi-polynomial method.

A: y''-3y'-4y=0 D2-3D-4=0 D2 -4D+D-4=0 (D+1)(D-4)=0 D=-1,4 Complementary function =c1e-x +c2e4x

Q: The system of ordinary differential equations given by x'1 = ax1 + bx2 , x'2 = bx1 + cx2 has the…

A: We have the given system of ordinary differential equations is x'1 = ax1 + bx2  x'2 = bx1 + cx2 In…

Q: Question 3. Consider the eigenvalue problem U"(x) + XU (x) = 0, 0<x< l with the mixed boundary…

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Q: -1-9 cos² 6t + 12 sin 6t cos 6t -12 sin² 6t+ 9 sin 6t cos 6t y' = that has periodic (therefore…

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Q: Consider the initial value problem (a) Find the eigenvalues and eigenvectors for the coefficient…

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Q: x=12²2 ²1x X find the eigenvalues and eigenvectors -Classify the critical point (0.0) as to type

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Q: 3. Use the concept of eigenvalues and eigen 3 2 4 (a) X'= 2 0 2 X 4 23

A: According to Bartleby guidelines I have completed the one among them

Q: What is the eigenvalue for the eigenfunction e^4ix of the operator ((d^2)/(dx^2))+(d/dx)−4i?

A: The solution is given as