3. Verify orthogonality for the following ODE and find the eigenvalues and eigenfunctions: (x²)² + (a + 1) == 0 +(a + 1) = 0 y(1) = 0 y(e) = 0 x3
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- Find the eigenvalues and eigenvectors of dx dt 1 = (2-3)x Number of eigenvectors: Choose one Choose one One Two XGraph the phase plane (xy-plane) for the following system of ODE’s using eigenvalues and eigenvectors.Find the eigenvalues and the eigenvectors of A and A-1 (check the trace!): A λι = X2 = 2 A-1 = [ -0.5 11 0.5 ]: λι = with x1 = and 9. with x2 = with x1 = and 9. X2 = with x2 =
- Consider the function: f (x,y) = 2x² - 4x - xy² + 2y² - 3. You are given the following stationary points: (2, −2), (1, 0) and (2,2). Use the eigenvalue test to classify each of the stationary points.Find the eigenvalues and the eigenvectors of A and A²: A 1 3 = 2 0 λι 2 = A² = 2 -31 6 λι 2 with X1 and with x2 with X1 ။ = with x2 andFor #1(c), use diagonal factorization please.
- Compute the other eigenvector. And draw each of the eigenvectors and the transformed vectors (with A) on the graph below.For each of the following ODEs determine if the eigenvalues are (a) real and distinct, (b) repeated, (c) complex conjugate pairs: 1. + 2x + 3x = 0 2. + 4x + x = 0 3. x + 4x + 4x = 0 4. x+3x0Q1. Find, for the matrix B, the eigenvalues and their corresponding eigenvectors B =[-₂ -¹3]