4. For the Sturm-Liouville problem y" + xy = 0, y(0) = 0, y'(L) = 0 find the eigenvalues and eigenfunctions. Verify orthogonality.
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Q: 9. Use the method of eigenfunction expansions to solve the problems: a. y" = x², y(0) = y(1) = 0.
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Q: 3) Solve KHG30 r(t) = y(t) = r(0) = 2, y(0) = 3 (Using Method of Eigenvalue/Eigenvectors)
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Q: One solution of t + 2 t =x² + t + 2 is x₁ (t) = t. Find a second independent X1 - x = 0 t² solution.
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- Find all positive eigenvalues and eigen functions for the Sturm-Liouville y" + xy = 0, y'(0) = 0, t = (0, π) Y(T) = 0.Q1) Consider the problem y"+y= 0, y (0) = 0, y(1) = 0. a) Find the eigenvalues and the eigenfunctions. b) Expand f(x)=x using the above functions.Consider the Sturm-Liouville problem: y" + Ay /(-L) 0, -LSolve the eigenvalue problems: Ly ₁²y = xy dr² for the two following sets of boundary conditions i. y(0)) = 0 and y(3) = 0 Ak = Yk (x) ii. y(0)) = 0 and y' (3) = 0 Ak = Yk (x) **NOTE: you must leave your answers for the eigenfunctions written in terms of X₁, rather than writing them out explicitly in terms of k, otherwise they won't be recognised as correct***3 Find the eigenvalues and eignturation of sturm-to- "Y+2y=0; y(a)=0 Ỳ (3) = 8I need to revise for tomorrow it’s more complicated than I used to do, helpFind the eigenvalues and eigen functions of the Strum-Liouville problem u" + Au =0, 0sx3- Solve the problem P.D.E. u, = uxx 05. Given the system X" - ()* 10 2 (a) Find the general solution. (b) Find the solution that satisfies the initial condition (x(0), y(0)) = (0, –7). Report your solution as one vector.2. Find the eigenvalues and eigenfunctions. Verify orthogonality. Show details of your work. y" - 2y' + (A + 1) y = 0, y(0) = 0, y(1) = 0Find the eigenvalues , 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" + 2y +(2+1)y = 0, y(0) = 0, y(9) = 0 Yn(x) = 2 ²n² 18 Need Help? Read It n = 1, 2, 3, ... n = 1, 2, 3,...Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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