(b) Consider the initial value problem -2 1 z7) = 3 Find ö(t), writing your answer...
(a) Solve the initial value problem 2" +2r' + r = 8(t - 2), z(0)=1, 2'0) = 2 (b) Consider the initial value problem -2 -5 z(0) = 3 Find ö(t), writing your answer as a single vector. k 2 k 0 1] (c) Consider the matrix 0 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions?...
Kindly do these asap and clearly. Thanks (b) Consider the initial value problem ܚܕ ܠ ܂ (0) Find (t), writing your answer as a single vector. 1 k 0 (c) Consider the matrix 0 k 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A-1 exist? iii. For what value(s) of k does the linear system Aõ= 7 have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue?...
Consider the initial value problem (a) Find the solution u(t) of this problem. u(t) = b) For t > O find the first time at which lu t = 10 A computer algebra system is recommended. Round your answer to four decimal places.) 回Show My Work (optional:@
(1 point) Consider the initial value problem dx [2 -5 dt 15 2 (a) Find the eigenvalues and elgenvectors for the coefficient matrix and λ2-2-51 (b) Solve the initial value problem. Give your solution in real fornm. x(t)
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector UI, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. c. Solve the original initial value problem. n(t)- 2(t)
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
(1 point) Consider the initial value problem (a) Find the eigenvalues and eigenvectors for the coefficient matrix. di = , and 12 = (b) Solve the initial value problem. Give your solution in real form. X(t) = Use the phase plotter pplane9.m in MATLAB to answer the following question. An ellipse with clockwise orientatio 1. Describe the trajectory.
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answer in terms of w,y, z. Problem 4 Solve the above problem by applying Laplace transform to the whole system without transferring it to a single equation. Do you get the same answer as in problem1? (Hint: Denote W(s), Y (s), Z(s) to be Laplace transforms of w(t),...
7.6(3) (1 point) Consider the Initial Value Problem -L* 4)*, x0=[!] (a) Find the eigenvalues and eigenvectors for the coefficient matrix. 1 ,01 = , and 12 = (b) Find the solution to the initial value problem. Give your solution in real form. x(t) = Use the phase plotter pplane9.m in MATLAB to help you describe the trajectory An ellipse with clockwise orientation 1. Describe the trajectory.