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- Find the smallest eigen value of (1+x)y" + y' + λy = 0, y(0)=0, y(1)=03 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 D
- Find the eigenvalues and eigen functions of the Strum-Liouville problem u" + Au =0, 0sxApply the eigenvalue method to solve the initial value problem3- Solve the problem P.D.E. u, = uxx 02. 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 youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage LearningCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning