Find the eigenfunctions of the Sturm-Liouville problem y" + y = 0, y(0) = 0, y' (L) = 0, and make the set an orthonormal set of eigenfunctions.
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- Consider the Sturm-Liouville problem: y" + Ay /(-L) 0, -LConsider the system of differential equations For this system, the smaller eigenvalue is (-39/10) [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y'= Ay is a differential equation, how would the solution curves behave? • All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) and the larger eigenvalue is The solution curves would race towards zero and then veer away towards infinity. (Saddle) The solution curves converge to different points. The solution to the above differential equation with initial values (0) = 4, y(0) = 3 is (t)= (49/12)*e^((-9/10)*t)-(1/12)*e^((-19/10)*t) y(t) = (49/12)*e^((-9/10)*t)+(5/12)*e^((-19/10)*t) da dt dy dt = -1.4x +0.75y, = 1.66667 3.4y. (-9/10)The eigenvalues of the initial value problem y' +Ây=0, y(0)=0, y'(7)=0 are a) , = vn, for n=1,2,3,... b) 1, =n², for n=1,2,3,... c) 2, = 2n, for n=1,2,3,... d) , =, for n=1,2,3,... 2'Determine the eigenvalues and corresponding eigenfunctions for the following boundary value problem: Domain xe (0,7) X" + AX = 0 with boundary conditions: X(0)=X'(7)=0The eigenvalues of x²y*- xy' - ày = 0, y(1) = 0, y(e) = 0 s Hint:[Use only case 3] (a) A, =1+ n2,2 n= 1,2,3,.. 4 (b) A, --1- ( An = -1-n?,2,n = 1,2,3,.. n=1,2,3,... (c) An =1+n?,2,n (e) None of these ,n= 1,2,3,...I need to revise for tomorrow it’s more complicated than I used to do, helpGiven the correct eigenvalues above and the eigenvectors below, what is the general solution of the system: K₁ = (²₁) x² - (- ₁²) X 1 2 X' 2 cos2t X = C₁ (22) e¹ + C₂ (co2) tet -sin2t) )e² sin2t O A (Cost) et + c₂ (sin2t) tet -sin2t. X = ₁ X = C₁ O B 1 (Cost) et + C₂ (cos2t) et 2 -sin2t sin2t. cos2t X = C₁ (0522) e² + c₂ (Sin2t) et -sin2t cos2t) O DDo only 4th part U may need part 3rd I have uploaded half part of 3rdFind the eigenvalues and eigen functions of the Strum-Liouville problem u" + Au =0, 0sxFind the eigenvalues and eigenfunctions yn(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.) x²y" + xy' + 2y = 0, y(1)= 0, y(e) = 0 2n = Yn(x) = , n = 1, 2, 3, ... , n = 1, 2, 3,...Find all the eigenvalues and eigenfunctions of the Sturm-Liouville problem. Use the integral inner product to verify the orthogonality of the eigenfunctions. y" + xy = 0, y (0) = 0, y (3) = 03- Solve the problem P.D.E. u, = uxx 0Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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