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Cosider the second order initial value problem y = y'exp(-3 y) - 2+y+12, 1€ [2,4), y(2)...
In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem (+3)y' 2y 0 subject to the initial condition y(0) 1. Since the equation has an ordinary point at z 0 it has a power series solution in the form We learned how to easily solve problems like this separation of variables but here we want to consider the power series method (1) Insert the formal power series into...
How to do question B 2,3,4,5? 3. a) Find the solution v ote ordinary diferetinl equation with the initial coditions: b) i) Recast our third ord ODE into a system af first order ODEs af the formA.v, where v' = dv/dz f(v) and v = (y, y,y")". You should show all working to find the corresponding matrix A. Do not solve the system. 4 mark Solve it only by hand and show your complete work. Do not use a calculator...
Convert the second-order initial-value problem into a system of first-order initial value problems. y'' + 7y' + 2y = e^(3x) y'(0)=1 y''(0)=1
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...
Would someone help me with the last 3 questions here, I got the previous ones but need help with the last 3 in red. Thank you Transcribed: Now that you nd a rst order system of ODEs, you can solve it using the Huens method ac- cording to the material you covered in computational module 2. A template of the code which will help you to get started is also available. Attach the complete code as a pdf page to...
Problem 1 Consider two first order low-pass systems connected in parallel: -2u The objective is to determine a second order ODE describing the variable y by manipulating the differential equations (no transfer function techniques are allowed). Answer the following series of questions: 1. (2 points) Write the variable y in terms of i and 2 2. (6 points) Determine the relationship between y, j, and z1, z2 and u. Write your final expression in a matrix-vector format: ? 01 ??...
(5 points) Find all 5 equilibria for the system of first order ODES dx = x(4-y-12) dt dy = y(x2-1) dt
Problem 2. For the following system described by the difference equation where y[-1-y[-2] = 0 and x[n] = 2u[n]: a. Draw a block diagram of this system using delays, multipliers, and adders b. Determine the impulse response of the system, h[n], and plot it in MATLAB for n = 0, 1, ,20. (Hint: use Euler's Formula to simplify) c. Is this system stable? d. Determine the initial conditioned repsonse, in. e. Find the total response of the system, yn nln....
(1 point) In this exercise we consider the second order linear equation y" + series solution in the form y = 0. This equation has an ordinary point at x = 0 and therefore has a power y = cmx". n=0 We learned how to easily solve problems like this in several different ways but here we want to consider the power series method. (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn...
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h 0.05 Find the value of x(0.4) for the coupled first order differential equations together with initial conditions with step size 0.1: 2. dt t+x 3. dx dt = y, dy dt x(0) = 1.2 and --ty +xt2 + y(o) 0.8 Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h...