1. Given the system of differential equations (28)) = (3-3) ().compute the eigenvaluesand eigenvectors, sketch the direction field and stright-line solutions, and state the generalsolution to system. For each eigenvalue specify a corresponding straight-line solution. Findthe particular solution with initial condition (x(0), y(0)) = (-4,-8).YX

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Answered: 1. Given the system of differential…

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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Solve the system of differential equations{x'=29x−50yy'=15x−26y{x′=29x-50yy′=15x-26yx(0)=−13, y(0)=−8x(0)=-13, y(0)=-8The lesser of the two eigenvalues isIts corresponding eigevector is ⟨a,−3⟩⟨a,-3⟩. What is aa?a=a=The greater of the two eigenvalues isIts corresponding eigevector is ⟨2,b⟩⟨2,b⟩. What is bb?b=b=The solution to the system isx(t)x(t) = y(t)y(t) =
3. Classify the given partial differential equation as hyperbolic, parabolic, or elliptic. a. а2u azu J2u дх2 дхду дуг + + = 0 b. д2u a2u az = at2 ?х2
Consider the linear system X' = [223] -2 X. 1. Show that the eigenvalues of the given system are complex. 2. Find the general solution of the system.
4. For the Sturm-Liouville problem y" + xy = 0, y(0) = 0, y'(L) = 0 find the eigenvalues and eigenfunctions. Verify orthogonality.
A linear systems of differential equations is to be solved using eigenvalue method. Determine the eigenvalues of the system and obtain corresponding eigenvectors to get the general solution. (Hint: You may need to define a new variable. ) y' = x x" = 3x + 2y
у R[0, 1] be the set of all Riemann defined on [0,1] and Let Integrable functions Let & be defned by d (hy) = So I fa - gwoldx for all points PigeR[0, 1]. Explain why is (R50, (I) / not a metric space
Given 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
Solve the 2nd-order homogeneous Cauchy-Euler equation r²y + 23ry + 121y = 0 The linearly independent solutions are 3/2= and the general solution of the equation is y (r) = where ei, and are arbitrary constants. (Note: Let 1 and 2 be two solutions of the auxiliary (characteristic) equation. (1) If m1m2, write /1 and 1/2 = ""; ® and 2 In (r); and = (ii) If m1m2, write /1 = (iii) If m₁ = a +bi, and m₂ = a-bi, write 9/1 = cos (bln (r)) and 2 = sin (bln (z)).) symbolic formatting help
determine eigenvalues and eigenvectors if the eigenvalues are real. Also, determine the general solution of the following linear systems of differential equations:dx/dt = ax + by,dy/dt = cx + dy.
which is the solution vector x(t)=(x(t)) of differential equation system (y(t))
Q1) Solve the following system of algebraic equations using matrix inverse method. 6 30-0 Q2/ Solve the following differential equations. 1) + y² - 4: 2) 7+3 / +2y=0 Q3/ Find points of intersection for the following curves. 1- r = 1+ cos 0, 2- r = 1 + sin 0.

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