For a homogeneous constant coefficient linear differential equation dy an dn-ly + an-1 dan-1 dy +...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
For a homogeneous constant coefficient linear differential equation d"y an dn-ly + an-1 dan-1 dy + a1 + aoy = 0 ... dr" dx the auxiliary equation is the polynomial equation anr" + an-1r"++ a1r + ao = 0. We are interested in finding the roots of this equation. For example, for the equation d?y 10- + 25y = 0 dx? d'y dx4 has auxiliary equation r4 – 10r2 + 25 = 0. Solving for r, we know there must be four roots. The four roots are r = V5, V5, -V5, - V5. Notice that the two distinct roots have multiplicity two so there are four roots to this 4th order equation. It can also happen that complex numbers may appear as the roots of an auxiliary equation. For example, the auxiliary equation, with variable r, for d?y dy - 10- dx + 41y = 0 is ^2 - 10r +26 = 0. dx? The roots of this equation, entered as a comma separated list, are r = 5+6i,5-6i For a homogeneous constant coefficient linear differential equation d"y an dn-ly + an-1 dan-1 dy + a1 + aoy = 0 ... dr" dx the auxiliary equation is the polynomial equation anr" + an-1r"++ a1r + ao = 0. We are interested in finding the roots of this equation. For example, for the equation d?y 10- + 25y = 0 dx? d'y dx4 has auxiliary equation r4 – 10r2 + 25 = 0. Solving for r, we know there must be four roots. The four roots are r = V5, V5, -V5, - V5. Notice that the two distinct roots have multiplicity two so there are four roots to this 4th order equation. It can also happen that complex numbers may appear as the roots of an auxiliary equation. For example, the auxiliary equation, with variable r, for d?y dy - 10- dx + 41y = 0 is ^2 - 10r +26 = 0. dx? The roots of this equation, entered as a comma separated list, are r = 5+6i,5-6i
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
In this problem. we are interested in finding out the efficiency of a BitTorrent- like P2P file sharing system . Consider two peers Bob and Alice. They join a torrent with M peers in total (including...
-
Two rival PE firms are interested in finding the same two start- ups. Each would prefer not to get into a bidding war with the other regarding either of the start-ups. Payoffs are given in the...
-
We are interested in the ordered probit model. Our data consist of 250 observations, of which the response are Using the preceding data, obtain maximum likelihood estimates of the unknown parameters...
-
Lewis and Associates has been in the termite inspection and treatment business for five years. The following is a list of accounts for Lewis on June 30, 2017. It reflects the recurring transactions...
-
What steps are required in the development of an ER diagram?
-
During 2011, Friesen Corporation is sued by a customer who slipped and fell on the company's property. As of 12/31/2011, the lawsuit has not been finalized. Friesen Corporation evaluates the...
-
Have world poverty and instability ended?
-
Goode Company has the following production data for selected months. Compute equivalent units of production for materials and conversion costs, assuming materials are entered at the beginning of...
-
A Tim Horton's Coffee Mug is moving along a level table towards the right as a result of having been pushed. If the Coffee Mug has a mass of 0.5 kg and the coefficient of friction between the coffee...
-
Consider a building with 3200 ft 2 of walls. Assume the ceiling is well-insulated and compute the energy loss through the walls based on the following materials, assuming an indoor temperature of 70...
-
5. Write a main function to Reverse the elements of queue "queueA" only using stack and queue operations. Assume all stack and queue methods are provided. The queue must be unchanged. You MUST use...
-
Repeat Problem 4 for the case when the temperature of the water tank increases linearly with time at a rate of \(r\). Data From Problem 4: The temperature of a steel sphere with initial temperature...
-
Find the state vector via the formal-solution approach. \(\dot{\mathbf{x}}=\left[\begin{array}{cc}1 & -1 \\ -4 & 1\end{array} ight] \mathbf{x}+\left[\begin{array}{c}1 \\ \frac{1}{2}\end{array} ight]...
-
\(\mathbb{A}\) Consider a second-order system \(Y(s) / U(s)=\omega_{n}^{2} /\left(s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2} ight)\). a. Write a MATLAB m-file to plot the magnitude of the system's...
-
A single-tank liquid-level system with inflow rate \(q_{i}\) as its input and liquid level \(h\) as its output is modeled as \(R A \dot{h}+g h=R q_{i}(t), h(0)=0\), where \(R, A, g=\) const. If the...
-
The mathematical model of a dynamic system is described by \[4 \ddot{x}+4 \dot{x}+5 x=\frac{10}{3} u_{r}(t), \quad x(0)=0, \quad \dot{x}(0)=\frac{2}{3}\] where \(u_{r}(t)\) is the unit ramp. Plot the...
-
Save Answer The frequency of shedding of vortices from a body owing to the flow of fluid past it depends on the length-scale of the body, the speed of the fluid flow, and the density and viscosity of...
-
Write a paper about how diet relates to breast cancer in women study design to use: case control study purpose & rationale the purpose of this final project is to utilize the methods and...
-
Let Mn be the n n tridiagonal matrix with all l's on the sub- and super-diagonals, and zeros on the main diagonal. (a) What is the spectral radius of Mn? Use Exercise 8.2.47. (b) Is Mn convergent?...
-
(a) Prove that if A is complete, so is A2. (b) Give an example of an incomplete matrix A such that A2 is complete.
-
Prove that Av = 0 for every vector v (with the appropriate number of entries) if and only if A = O is the zero matrix.
-
The mean free path \(\lambda\) of a molecule of gas is the average distance it travels before collision with another molecule. It is given by \[\lambda=C \frac{m}{ho d^{2}}\] where \(m\) and \(d\)...
-
A rectangular gate (width \(w=2 \mathrm{~m}\) ) is hinged as shown, with a stop on the lower edge. At what depth \(H\) will the gate tip? Water H 0.55 m 0.45 m P3.46 Hinge Stop
-
Gates in the Poe Lock at Sault Ste. Marie, Michigan, close a channel \(W=34 \mathrm{~m}\) wide, \(L=360 \mathrm{~m}\) long, and \(D=10 \mathrm{~m}\) deep. The geometry of one pair of gates is shown;...
Study smarter with the SolutionInn App