3. Find the eigenvalues and the corresponding eigenfunctions of the Sturm-Liouville system y" +ày = 0, (0) = 0, A7) +y (n) = 0.
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![3. Find the eigenvalues and the corresponding eigenfunctions of the
Sturm-Liouville system
y" +ày = 0,
(0) = 0, A7) + y (n) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc67557e6-cf86-4842-86bd-4f64217beb5f%2F7b65913a-b250-4f8c-919b-4ca2807ece55%2Ff2rrvr8_processed.jpeg&w=3840&q=75)
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- Please do number 5Find all positive eigenvalues and eigen functions for the Sturm-Liouville y" + xy = 0, y'(0) = 0, t = (0, π) Y(T) = 0.Find 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.) у" + Лу %3D 0, у(-п) %3D 0, у(п) %3D о 12k - 1 k = 1, 2, 3, ... Y2k – 1(x) = | k = 1, 2, 3, ... k = 1, 2, 3, ... Y2k(x) = k = 1, 2, 3, ...
- 9Consider the Sturm-Liouville problem: y" + Ay /(-L) 0, -LA 3×3 real matrix has three eigenvalues. One of them is λ₁ = Another is A₂ = 1 + i with eigenvector v2 - (3) = -1 with eigenvector v₁ = (a) What is the third eigenvalue and its corresponding eigenvector? (b) Find the general solution to x' = Ax, in purely real form. (c) Find the solution to x' = Ax subject to initial condition x (0) = (:). (6) 1The eigenvalues of the system (x +1]y" + 2xy' - 4y = 0 are A. None of them B. x = -i and x = i C. Å1 = -3 and Az = 4 %3D D. A1 = -4 and Å = 2 O E. x = -1 and x = 1 %3D3 Find the eigenvalues and eignturation of sturm-to- "Y+2y=0; y(a)=0 Ỳ (3) = 8Given 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 DRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,