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7/7 7. (20 pts) Solve difference equation Yk+2 + 4yk+1 + 4yk = 0, yo =...
1. (20 pts) An LTCI system is defined by the equation *0) + 1) + 4y0) = 10) (a) find the characteristic polynomial, characteristic function equation, characteristic root and characteristic modes of this system. (b) Find yo(t), the zero-input component of the responses y(t) for t > 0 with initial conditions yo(0) = 2 and y(0) = -1. 2. (20 pts) Repeat the previous problem if Vt) + 9y(t) = 351) + 2FE) and yo(0) = 0, Y%(0) = 6.
Solve the matrix-eigenvalue equation Question 1 (6) That is, solve 1 1 0 20 -1 0-0 /2 and -1/2. to find the eigenstates of §, and show that the eigenvalues are s Question 2: Solve the matrix form of the Schrödinger equation Hu E/ to find the eigenstates and energy levels of the Hamiltonian matrix ви Во ( 1 0 А -и- В %3 -8иBos. (7) 0 2 Solve the matrix-eigenvalue equation Question 1 (6) That is, solve 1 1...
5. Take the difference equation Yn = -1 + 31, Yo = 40 and do the following: A. Generate the first 5 values of the list using the difference equation. Show how you generated the values. Place a box around your final answer. (2 points) B. Solve the difference equation. Show all the steps that you performed to arrive at your answer. Show the general formula that you used. Place a box around your final answer (4 points) C. Use...
2. (20 pts) Solve the initial value problem. (Note that the equation is a Cauchy-Euler equation.) 9x2y' + 3xy + y = 0, y(1) = 1, y (1) = -1
solve each equation algebraically: a) 3+7e^2x=24 b) 2^x+5=7^3x+1 c) 3^(2x) - 3^(x) - 20=0 d) log x + log (x-5)=2 ^6 ^6 e) log(x+2)-log(x-1)=1 f) ln(log (x^2 + 2x))=0 ^3 d og, 71 Solve each of the exponenti a tions call the as well as a decimal approximation to the nearest the get the approximated solutions Yo d ac t o a) 3+72-24 d) 3 -3-20 - 0 get the approximated solution a) loe +log.-5) = 2
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5 (20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
MMatlab Please Homework Due Nov. 19 1. Solve the ODE system (Van der Pol's equation) below using the function ode45 and the initial values y,0) = y20) = 1. dyi at = 32 wat = u(1 – y})yz – yı where u = 1 and solve between t = 0 to 20. dt Hint: for this equation, your initial conditions yo will have 2 values. For the odefun, you will have a one output, two inputs (t and y), and...
For each of the following difference equations (i) obtain the general solution; (ii) solve an initial value problem: (iii) solve for the fixed point if it exists and indicate whether or not yk converges to the fixed point. For each of the following difference equations (i) obtain the general solution; (ii) solve an initial value problem: (iii) solve for the fixed point if it exists and indicate whether or not yk converges to the fixed point.
Let Xo, X1, n 0, 1, 2, . . . . Show that YO, Yı , matrix ,... be a Markov chain with transition matrix P. Let Yn - X3n, for is a Markov chain and exhibit its transition
Solve the difference equationy(n + 2) + 4y(n + 1) +3y(n) = 3n with y(0) =0, y(1) = 1