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- This was incorrect last time I asked so I will try again, thank you!.ÿ' = -[3. a. Find the eigenvalues and eigenvectors for the coefficient matrix. i 3/1-1/16 5 5 A₁ = i = 1 • Find the real-valued solution to the initial value problem yí = ly/₂ = Use t as the independent variable in your answers. 31(t) = 11 y2(t) = -15 15 2 -5 -3 3y1 + 2y2, -5y1 - 3y2, y. and A₂ = -i 9 y₁ (0) = 11, Y2(0) = −15. 9 V2 = T 1 i 3/4 + 1/4 5 351. (a) What are A, X and x' in matrix form x' = AX of the system of differential equations { FO (b) Find all eigenvalues and eigenvectors of A. (c) Find exponential solutions of the system of differential equations. (d) Verify your solutions. x₁ = 3x1 x2 = 5x1 + 2? x2
- 2n+1 If x,=cos TEX, are the eigenfunctions for the following IBVP +co 0Find 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) = 81. Find real-valued fundamental solutions of the differential equation x' = Ax, where matrix A has eigenvalues and eigenvectors - [₁4] - 6.2) A₁ = −2+i V₁ = A2 = -2-i V2 =3- Solve the problem P.D.E. u, = uxx 0Consider the following matrix A = 5 7 0 -2 (a) Find the eigenvalues and the eigenvectors of this matrix. (You need to show how you find them.) (b) Using the eigenvalues and the eigenvectors of A, solve the system of differential equations ' = AT.Recommended 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,