Find the eigenvalues, and eigenfunctions y, (x) for the given boundary - value problem. PH09 (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) x? y +xy' +2y= 0, y(1) = 0, y'(e) = 0 an = n = 1, 2, 3,... yn(x) = n = 1, 2, 3,
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- Solve Q2 using Eigen values and eigen vectorsFind the eigenvalues 1, and eigenfunctions y,(x) for the given boundary-value problem. (Give your answers in terms of k, making sure that each value of k corresponds to two unique eigenvalues.) y" + ly = 0, y(-a) = 0, y(n) = 0 22k -1= k = 1, 2, 3, . -. Y2k – 1(x) = k = 1, 2, 3, ... k = 1, 2, 3,... %3D Y2k(x) = k = 1, 2, 3,- -. earch 耳 合 PrtScn. F8 Home F9 DII F2 F3 F4 F5 F6 F7 & 3 5 6 7 8 R Y4. Solve given that x' = Ax + A has eigenvalues -2 and -6. -3 3 1 5
- please do b)Find eigenvalueFind the eigenvalues 1, and eigenfunctions y,(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y" + Ay = 0, y(0) = 0, y(n/3) = 0 1, = 4n?, Vn = sin(2nx), n= 1,2,3,.. a. A, = 36n?, V,=sin(6nx), n= 1,2,3,... A, = 25n?, V,= sin(5nx), n= 1,2,3,.. b. C. A, = 9n?, Vn = sin(3nx), n= 1,2,3,.. d.
- I try to use the eigenvalue to find eigenvector, and I've already found the relation between x and y. I can substitute x=1 and get y=-i, but the solution provided is substituting x=-1 and get y=i. There is a problem, how can I know which value of x should I choose?Q.6 Use eigenfunction expantion methodto solve: _1 y(1) = e, y(e)=0 :Reduce homogereaus Fredhlölm snteqral equation 2e D1x)-11kしxっ)ult)1 Where, k (1st) = sinhtsinh (x-1) ,t za41 sinh1 Solve the resulting BYP for & Eigen fila ction. Eigen Yalues
- Find the smallest eigen value of y" + λy = 0, y(0) = 0, y(1)= 0 , give the correct answer only else downvote ( Hint substitution )I have attached an image of the graphical method.Consider the linear system X1 = and Find the eigenvalues and eigenvectors for the coefficient matrix. A₂ = 0 JI ← A, V₁ 9 V2 = 81 = = -3 6 - - 4 x. help (numbers) help (matrices) help (numbers) help (matrices) For each eigenpair in the previous part, form a solution of a' = Ax. Use t as the independent variable in your answers.