22 -68. The general solution of x' =x is: (Hint: 6 is an eigenvalue.)2-1-3-2-1-231(a) x = Cieốt+ Cze-2t+ C33(b) x = Ce6t1+ Cze-2t2(c) x = Ce6t+ Cze-2t+ Cze-2t2223(d) x = Cie6t+ C3 te-2t21+ Cze-2t-2(e) None of the above.

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Answered: 2 2 -6 8. The general solution of x' =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. Use the eigenvalue method to find the general solution of the system x₁ = X1 X2, x2 = 10x₁ + x2.
Use eigenvalue metnoa to nna requirea solution of the following system. x₁ x2 = −4x₁3x2 – £3 and - x3 = 2x1 + x2 = x3 O = = 4x₁ + 4x2 + 2x3. The initial conditions are ₁ (0) = 0, x2 (0) = 1 and 3 (0) = 4. 2 -8-8-0 -2 + sin 2t -2 +e² 3 7 x(t) = cos 2t 6 6 4 2 H H+O -5 +e²t 4 3 x(t) = cos 3t -3 + sin 3t x(t) = cos 3t x(t) = cos 2t 2 -#-#-D -2 + sin 3t 3 4 2 -6 -4 + sin 2t 6 3 2 tel + e 0
How do you get to the reduced form and then get the eigen vector in this problem?
+5Ux2 Ux₂ -u +10u=0 is of Kitz x3x3 6. Show that the equation 3u-2u₂ +2u -2u +3u xx2 elliptic type by determining that the matrix A [see (3.3.2)] has the eigenvalues 21,2₂3, 2₂4 Determine a transformation (3.3.14) that yields the equation 6 +3162 +41 55 + 2u+ + √2/24 √√6 u +10u = 0. 15 -5545
Need Handwritten SOLUTION.Need Solution in 30 Minutes .Solve Q2 only .Thankyou!!
Use a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion - Row reduction -Integration5.
Use (a) to solve the system x = (: :) . Х. -8 7 NB: Real solutions are required. Hint: Recall that if the roots of C(A) = 0 occur in complex conjugate parts, then any one of the two eigenvalues yields two linearly independent solutions. The second will yield solutions which are identical (up to a constant) to the solutions already found. a) is as follows Show from first principles, i.e., by using the definition of linear independence, that if x+iy, y # 0 is an eigenvalue of a real matrix A with associated eigenvector v = u + iw, then the two real solutions Y(t) = et (u cos bt – w sin bt) and Z(t) = eat (u sin bt + w cos bt) are linearly independent solutions of X = AX.
The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x₁ = 7x₁ + x₂ + x3, x2 = - 13x₁ - 7x₂ -X3, X'3 = 13x₁ + 13x2 + 7x3 * A What is the general solution in matrix form? x(t) = Jiry
- (1-3). Determine the eigenvalue and corres- 3. a) Given the matrix A = ponding eigenvector and generalized eigenvector of A. b) Determine the general solution of the system of linear differential equations: x₁ = I₁=I₂ x₂ = x1₁+3x₂
Find the general solution of the following inhomogeneous systems. Use either eigenvector decomposi- tion or undetermined coefficients method. These problems can be solved by hand, but you can also use technology to assist you at any stage. When using technology always report on what function you use. **BHRAIBHS] -2 5 5 -2 (a) = (b) + = 2 -1 **[G]HBKH[**] 3 -2 3e + -2t cos 3t
can someone explain this for me, please ?

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2 2 -6 8. The general solution of x' = x is: (Hint: 6 is an eigenvalue.) 2 -1 -3 -2 - 1 -2 3 1 (a) x = Cieốt + Cze-2t + C3 3 (b) x = Ce6t 1 + Cze-2t 2 (c) x = Ce6t + Cze-2t + Cze-2t 2 2 2 3 (d) x = Cie6t + C3 te-2t 2 1 + Cze-2t -2 (e) None of the above.