Problem 3 (Systems of Differential Equations) For ordinary differential equation x (t) + 4x' (t) +...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Problem 3 (Systems of Differential Equations) For ordinary differential equation x" (t) + 4x' (t) + 5x(t) = 0 with initial conditions x(0) = 3 and x'(0) = -5, a) Use the four order Runge-Kutta method with step size h = 0.1 to solve the differential equation over the interval [0, 5] in MATLAB. HINT: By defining y = x', the second order ODE can be written as a set of first order ODE (which you now know how to handle) given by x' = y (Eq. 1) y' = -5x - 4y Eq. (2) with initial conditions x(0) = 3 and y(0) = -5. These two first order ODES can then be solved simultaneously the four order Runge-Kutta method with step size h = 0.1. The function y(t)=x'(t), is just an intermediate step needed to compute the function x(t) we are solving for.. b) Compare the numerical solution with the true solution x(t) = 3e-2t cos(t) + e-²t sin(t) in a MATLAB plot over the same interval. (Hint: define y = x') Problem 3 (Systems of Differential Equations) For ordinary differential equation x" (t) + 4x' (t) + 5x(t) = 0 with initial conditions x(0) = 3 and x'(0) = -5, a) Use the four order Runge-Kutta method with step size h = 0.1 to solve the differential equation over the interval [0, 5] in MATLAB. HINT: By defining y = x', the second order ODE can be written as a set of first order ODE (which you now know how to handle) given by x' = y (Eq. 1) y' = -5x - 4y Eq. (2) with initial conditions x(0) = 3 and y(0) = -5. These two first order ODES can then be solved simultaneously the four order Runge-Kutta method with step size h = 0.1. The function y(t)=x'(t), is just an intermediate step needed to compute the function x(t) we are solving for.. b) Compare the numerical solution with the true solution x(t) = 3e-2t cos(t) + e-²t sin(t) in a MATLAB plot over the same interval. (Hint: define y = x')
Expert Answer:
Answer rating: 100% (QA)
a To solve the differential equation using the four order RungeKutta method with step size h 01 in M... View the full answer
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
Posted Date:
Students also viewed these accounting questions
-
Equation (10.2) can be written as a system of two equations: v11 + rv12 = 1v11 rv11 + v12 = 1v12 Where r = r12 = 0.97135 is the correlation between x1 and x2. Find the first eigenvector, v1, by...
-
The interval (2, 5) can be written as the inequality _________.
-
A linearly polarized wave can be written as the superposition of two oppositely circularly polarized waves that have equal amplitudes, show that for the case considered. the plane of linear...
-
Consider an electric motor with a shaft power output of 20 kW and an efficiency of 88 percent. Determine the rate at which the motor dissipates heat to the room it is in when the motor operates at...
-
Since the United States has an unemployment compensation program that provides income for those out of work, why should we worry about unemployment?
-
If 4 x = 7, what does 42x equal?
-
A parallel-plate capacitor connected to a battery maintaining a potential difference \(V\) across the capacitor initially stores electric potential energy \(U_{1}^{E}\). If the plate area is doubled...
-
After watching the video on mining in Australia, discuss the following: 1. Is the Chinese firm interested in global sustainability? 2. How has the Chinese firm categorized the Aboriginal people as a...
-
Answer the question by showing the calculation procedure. Verified the answer by using the MATLAB coding. Submit all the answers (calculation procedure & MATLAB code) to MS Team. For all of the...
-
Create a concept map that depicts your assumptions and findings of the theory-practice gap. You are a staff nurse working in an intensive care unit and assigned to care for a 75-year-old African...
-
Let a stock's return follows the below model: Yt = 0.01 +0.2yt-2+ & where & ~w.n. (0,0.2) a) What is the return yt's mean and variance? b) What is and 2 ?
-
Whats wrong with expressions such as necessary prerequisite and big in size?
-
The following are the pillars of the Islamic contracts except: a. Legal capacity of contracting parties. b. Offer and acceptance. c. Suitable, known, and existing subject matter, with some exceptions...
-
Imagine that the spouse of a coworker recently died in an automobile accident. Write the coworker a letter of sympathy.
-
Analyze a brand profile on Facebook or Twitter. Identify four types of social media marketing tactics they have recently used.
-
Smith and Quarter Ltd. experienced the following events during the first quarter of 2006: 1. The annual sales catalogue was developed and provided on-line, at a cost of $1,000,000. 2. Programming and...
-
Clara owns a fine dining restaurant in Macau. Last year, her sales were not as high as she would have liked. To help increase her performance, Clara decided to hire a consultant, Dino, to help...
-
If your school has a subscription to the FASB Codification, go to aaahq.org/ ascLogin.cfm to log in and prepare responses to the following. (a) What is the stock dividend? (b) What is a stock split?...
-
A certain radioactive material is known to decay at a rate proportional to the amount present. Over a 50-year period, an initial amount of 100 grams has decayed to only 75 grams. Find an expression...
-
For each equation in Problems a to b, express the general solution of the nonhomogeneous DE a the sum of a particular solution (each is a polynomial in t) and the general solution of the...
-
For an invertible 3 Ã 3 ma-trix A, we can write, using the Cayley-Hamilton Theorem, A3 + bA2 + cA + dl = 0. where b, c, and d are coefficients of the characteristic equation of A. If we...
-
Ed owns Oak Knoll Apartments. During the year, Fred, a tenant, moved to another state. Fred paid Ed \($1,000\) to cancel the two-year lease he had signed. Ed subsequently began renting the unit to...
-
Sally W. Emanual, a teacher, had the following dividends and interest during 2022: Additional information pertaining to Sally Emanual includes The taxable portion of the pension is \($7,000.\) Sally...
-
What is the first day that an individual could sell a capital asset purchased on March 31, 2023, and have a holding period of more than one year?
Study smarter with the SolutionInn App