z(t) y(t) 2 0 (22 points) Find the general solution to3"(1)-Ax(t), where A = | 1-2...
Find the general solution. 2. Find the general solution. X' = AX A= 1 1 0 1 0 1 0 1 1 Note: X = [X1 22 23 x3]".
find a general solution z?y" + xy + (22 – 5) = 25/2 x > 0
Use the variation of parameters formula to find a general solution of the system x'(0) AX(t) + f(t), where A and f(t) are given -4 2 А. FU) 21 12 +21 Let x(t) = xy()+ X(t), where x, (t) is the general solution corresponding to the homogeneous system, and X(t) is a particular solution to the nonhomogeneous system. Find X. (t) and X.(1).
1.Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .2.Solve the given initial value problem. y'' + 3y' = 0; y(0) = 12, y'(0)= - 27 The solution is y(t) = _______ 3.Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them z"'+z"-21z'-45z = 0 A general solution is z(t) = _______
(25 PTS) 2. Find the general solution of x' = AX, where A = A = [5 -- }], x(0) = 1
(17 points) (a) Find the general solution of the differential equation y" (t) + 4y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (i) y(0) = 0, y'(0) = 1: y = (ii) y(0) = 1, y'(0) = 0:y= (iii) y(0) = 1, y(1) = 0:y= (iv) y(0) = 0, y(1) = 1: y = (On a...
4. (a) (8 points) Find the general solution of x' = Ax, for A= 2. Write the solution in vector form. 1-1 -3 (b) (4 points) Using your vector solution, write a matrix solution X(t). (c) (4 points) Using the matrix solution from part (b), determine en
Problem 22. Find the general solution to the Cauchy problem in implicit form (t sin(y)y' = 1 +cos(y) Solution. - - I cos(y(t)) = c.
(17 points) (a) Find the general solution of the differential equation y" (t) + 36y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (1) y(0) = 0,7(0) = 1: y= (ii) y(0) = 1, y'(0) = 0: y= (ii) y(0) = 1, y(1) = 0:y= (iv) y(0) = 0, y(1) = 1:y= 1 (On a sheet of...
For #1 and #2, find the general solution of the ODE system tX' = AX, t> 0. (You do NOT need to verify that the Wronskian is nonzero.) 1. A= ( 1)