2. for the following differential equation: y + 8y + 15y-u 30u, y(0)-1,y(0) 0,u(t)-t fort20 3....
2. For this differential equation y"(t) - 6y'(t) + 15y(t) = 2r(t), determine (4 points) a) Transfer function b) The poles and zeros of the transfer function c) Given that r(t) = sin(3t),y(0) = -1, y'(0) = -4, find y(t) using partial fraction expansion
Differential Equations
y(4) + 8y"+ 15y = 0
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
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) = _______
USING MATLAB
Please post code
1. Solve the 2nd order differential equation ?+89 +15y-sin(t), y(0)-1,?(0)-2 symbolically and numerically, and plot both results together over the time interval 0,10 sec. Provide appropriate labels on both axes, a title, and a legend that denotes each solution. Check your symbolic answer by using the Matlab DIFF function to compute the appropriate derivatives and then substituting them into the differential equation.
Given the following differential equation for some plant, dy +7.+ 15y = 2x(t) dt dt a. Find the steady-state output for a unit-step input. b. Find the step response of the plant; that is, solve for the output if the input is a step function, x(t) = u(t).
Matlab code for the following problems.
Consider the differential equation y(t) + 69(r) + 5y( Q3. t)u(t), where y(0) (0)0 and iu(t) is a unit step. Deter- mine the solution y(t) analytically and verify by co-plotting the analytic solution and the step response obtained with the step function. Consider the mechanical system depicted in Figure 4. The input is given by f(t), and the output is y(t). Determine the transfer function from f(t) to y(t) and, using an m-file, plot...
2. Find the solution of the second order differential equations: d2 +y = 0, y(T/3) = 0, y'(T/3) = 4 a. dx2 b. Y" - 8y' + 16y = 0, y(0) = 1, y(1) = 0
Solve the differential equation below using series methods. y' + 3xy' + 8y = 0, y(0) -1, y'(0) = – 5 Find the first few terms of the solution y(x) = axxk. k=0 ao = Preview ai Preview A2 = Preview = a3 = Preview 24 = Preview 05 = Preview
3. Find a solution to the following differential equation y" + y = sec3 t 5 t-2.
3. Find a solution to the following differential equation y" + y = sec3 t 5 t-2.