3.31. The BUPy" =4 [y-x), OLXLI, y (0)=0, yYW=2has the solution y(x) = e²/04-1) ²² (e²x²_e-2x) + x.a System,itse the finite difference method to reduce the problem tot.of theform Ay =1 with h = 4.

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Answered: 3.31. The BUP y" = 4 [y-x), OLXLI, y…

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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Suppose e2t and x2 = e2t X1 are solutions of the homogenous system x' = Ax. Use the method of variation of parameters to find the general solution of the nonhomogeneous system x' = Ax + f, where f =
2- If L(x, y) = ax + by2 is a Lyapunov function at the origin for the system * = y + x³, y = -x + y²³, a = b = 1. Then compute the expression: L(x, y) - 2(x + y4) = 3- If L(x, y) = ax² + by² is a Lyapunov function at the origin for the system x = 2x + xy², y = y(1-x²), a = b = 1, then this system is: (a) Stable (b) unstable (c) Asymptotic stable (d) stable if x 0.
Aşağıdaki sistemin 1 = 0 özdeğerine karşı gelen [x](t), y1(t), z1 (1)] çözümü X1(t)+z1 (t) için x1(t)+z1 (t) değerini bulunuz. [Evaluate for the solution yı(t) y1(1) [x1 (t), y1 (t), z1(f)] that corresponds to the eigenvalue 1 = 0 of the following system]. x' = -3x + 3z, y' = x – 4y + z, -2x + 2z. Lütfen birini seçin: 2 3. 4 LO
Solve for x and y the following system of simultaneous equations 2 In(x) = In(y) + In(9) e*ev = e3 subject to the restriction on x and y that x > 0, y > 0. a. Not in the list b. x=(9-/189)/2, y=(-15+/189)/2 C. x=(-9+/189)/2, y=(15-/189)/2 d. x=(-9-/189)/2, y=(-15-/189)/2
IV. Consider the system ſy = Does the system have a solution? That is, do the y = x graphs of y = e-* and y = x intersect? Justify your answer.
6. It is known that the general solution of the system *- )* = x is given by e³t+ [¹1] = C1 Use the method of Undetermined Coefficients for systems to find the form of a particular solution to the nonhomogeneous system x': A. x₂(t) = te a+eb+tc+d (B.x₂(t) = = teta+tb+c C. xp(t) = ea + e³t b+tc+d D. xp(t) = tea+t²b+tc+d E. x₂(t) = t'e' a+e¹b+tc+d = et. x+ 4e² Le+ Xce)= (ater ) t b, It = te¹ A + TB + C IB
1. Use Theorem 1 to solve the nonhomogeneous linear system *-[-])*+(1) x(0) = (6). with the initial condition =

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3.31. The BUP y" = 4 [y-x), OLXLI, y (0)=0, y1=2 has the solution y(x) = e² (c²4_1) ~² (p²x_p-²x) + X. itse the finite difference method to reduce the problem to a system of the form Ay zb with h = t.