Using the method of undetermined coefficients, find the solution of the system:

X'=AX + B

that satisfies the initial condition:

X(0)=( 0
1
-1).
A and B are matrices defined in the attached Notepad file.
Note: When solving the homogeneous soln, exhibit a fundamental matrix psi(t) and also the special fundamental matrix phi(t) satisfying phi(0)=I.

Solution Preview

Solution:For this system X'=AX+B (1)
We first need to know the given matrices A and B. If they are matrices with constant numbers, it is easy to solve them. For example, if we know A=P'CP where C=diag(a1,a2,...,an) and P'=P^(-1). P^(-1) is the inverse of P. Note that such P is called orthogonal matrix. Many matrices can easily find such matrix P such that A=P'CP.
Then substituting A=P^(-1)CP , (1) becomes
PX'=CPX+PB (2)
where C=diag{a1,a2,...,an}.
Let Y=PX and D=PB,then (2) is as follows
Y'=CY+D (3)
Obviously Y=-C^(-1)D is a special solution for (3). In order to solve (3), we only need to solve the linear diff. equations (4) as follows
Y'=CY (4)
In fact, IF Y=(y1,y2,...,yn), then (4) can rewrite as follows.
...

Solution Summary

This shows how to find the solution of a system using the method of undetermined coefficients.

An object is thrown horizontally from the top of a building at a height of 32.5 m above the ground, it hits the ground 65m from the base of the building. What is the initial speed? What is the velocity just before it hits the ground?

How can I proceed to solve the problem below?
The problem:
A projectile enters a resisting medium at x = 0 with an initial velocity Vo = 900 ft/s and travels 4in. before coming to rest. Assuming that the velocity of the projectile was defined by the relation V = Vo - kx, where V is expressed in ft/s and x in feet, determine

PROBLEM 1. Find a Lipschitz constant, K, for the function f (u, t) = u^3 + t u^2 which shows that f is Lipschitz in u on the set 0 ? u ? 2, 0 ? t ? 1.
PROBLEM 2. Show that the function f (u, t) = t u^(1/2), is not Lipschitz in u on [0, 1] × [0, 2].
PROBLEM 3. Find two solutions to the initial value problem y = |y|^(1/2) ,

The following problem was given as an example by the professor but I can't seem to come up with the same answer as he did.
The answer he got was C1 = -2 and C2 = 1/4
I keep getting C1 = - 1/4 and C2 = - 1/2
There are three possibilities 1) He's wrong 2) I'm wrong or 3) we are both wrong.
I need to know which it is.
Can you

The only force acting on a 2.4 kg body as it moves along the x axis varies as shown in Fig. 7-33 (attached). The velocity of the body at x = 0 is 4.0 m/s.
(a) What is the kinetic energy of the body at x = 3.0 m?
(b) At what value of x will the body have a kinetic energy of 8.0 J?
(c) What is the maximum kinetic energy attai

1 First find the general solution of the differential equation dy/dx = 3y. Then find the particular solution the satisfies the initial condition that y(1) = 4.
2 Solve the initial value problem dy/dx = y^3 , y(0) = 1
3 Find the center and radius of the circle described in the equation
2x^2+2y^2-6x+2y=3.
4

Enter formulas to calculate the requirements of this problem.
a. What is the average underpricing of this sample of IPOs?
Average underpricing FORMULA
b. What is the average initial return on my "portfolio" of shares purchased from the four IPOs I bid on?
Calculate the average initial

You have decided to purchase some shares of stock for $1000. After five years, the value of your purchase has grown to $2000.
a. Write a formula for the relationship between the future value of an investment and the initial investment amount. Use variables instead of actual quantities in your formula. Note what each variable