# order

1. ### Show that a transformation can be hapen of a system of 2nd order

Show that a transformation of a system of 2nd order is possible Hi there This is the exercise I'm trying to solve:  Show that the general ansatz -\sum_{1\le k,l \le n} A_{k,l}(x) \partial_k \partial_l u(x)+\sum_{1 \le k \le n}b_i(x) \partial u(x)+c(x)*u(x) (1) can be transformed to the...
2. ### 2nd order linear equation solving for a, with boundary conditions.

Hello I'm having problem solving the following: Let a be a real constant. Consider the equation y''+y'+ay=0 ]with boundary conditions y(0)=0 and y(6)=0. For certain discrete values of a, this equation can have non-zero solutions. Find the three smallest values of a for which this is the...
3. ### Differential Equations: Modeling with First Order Equations

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L/min, the well-stirred solution flowing...
4. ### Differential Equations: Modeling with First Order Equations

Hi I need some serious help with this problem, Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a...
5. ### Deriving Order Statistics

Let Y1, Y2, Y3, and Y4 be four independent random variables, each with density function f(y) = 3 (1-y)^2, 0 < y < 1, and 0 elsewhere. Derive the distribution function and the density function of Y1 and Y4. **Note: Although this is an ordered statistics problem, I am to derive and not plug into...
6. ### PFD, does order matter?

For an integral like \int_{0}^{1}\frac{1dx}{(x+2)^2(x-3)} I know the PFD would be written something like \frac{A}{(x+2)}+\frac{B}{(x+2)^2}+\frac{C}{(x-3)} But would that be the same as \frac{A}{(x+2)^2}+\frac{B}{(x+2)}+\frac{C}{(x-3)} ? I was going to type it into a calculator and test, but...
7. ### Basic order of operation question

Ok so this is pretty basic: -8-5(-8+4) = 12 so you do (-8+4) = -4 then you multiply the brackets, but heres where im confused, why do you 5* -4 =-20 and not -5*-20, because it is a negative 5 before the brackets right?
8. ### If the order of a group is prime number then the group is cyclic?

Let G be a group with a prime number p of elements. If a \in G where a \neq e, then the order of a is some integer m \neq 1. But then the cyclic group \langle a \rangle has m elements. By Lagrange's theorem, m must be a factor of p. But p is a prime number, and therefore m = p. It follows...
9. ### second order differential equations & Laplace

Hi all, this is my first post so please bear with me - anyadvice/support would be warmly welcomed. I have been doing some work on asimple RLC electronic circuit whose transfer function follows the standardsecond order transfer function. The forcing function (input) is a periodic square...
10. ### Group with p order elements

If G is an abelian group with order p^2, where p is prime.And for every elements in G have order p. Can I say that the group G is generated by 2 elements in G(every elements in G can be represented by the power of the product of a and b)??? I have tried the cases for p=2 but how about the...
11. ### First order logic! need help

hello guys. in a few days i have an exam. i have two problems to solve, but i couldn't do it. so please help me 1) show that "a" is false in a given interpretation if and only if "-a" (negation of a) is true in the same interpretation. and "a" is true if and only if "-a" false. 2) show that...
12. ### Origin of Numbers and Order

It starts with scratches on a rock (permanent) or in the dirt (temporary). Integers: 1, 11, 111, 1111, ….. Equality: 11 = 11 Order: 111 > 11, (1111, 1, 11) → (1, 11, 1111) Well Ordering Principle Pos Integers: 01, 011, 0111, … Neg Integers: 10, 110, 1110, ….. Addition: 011 + 0111...

1. Let A be the family of all subsets A of the natural numbers N where A has the following properties: A is finite and the greatest common divisor of the elements of A is 1. a. State whether or not each of the following subsets of N belongs to A: (2,3,8),(2,3,5,8),(2,5),2,3,4,5,...),(4,6,8) and...

15. ### Integrating factos - first order DE

Hi All, Could not solve this one: 12-x-3y+(x-y+4)y'=0 , y(0)=1 I tried to find an integrating factor in order to make it an exact equation but did not succeed. would appreciate your help!
16. ### Linear order isomorphism

Hello, I have a linear order relation defined on the product of set of complex numbers \mathbb{C}. \times \mathbb{C}. xRy \Leftrightarrow \Re x < \Re y \vee ( \Re x = \Re y \wedge \Im x \leq \Im y) I can prove that this relation is a linear order that's dense and without endpoints. But I...
17. ### Simple Question Regarding Order of Operations

Order of Operations 2(−4)2 + (6)(−4) − (−8) = 16 Why does this expression not equal -48? Should not it simplify to: = -16 * 2 + (-24) + 8 = -32 -16 = -48 To my understanding, I am following the PEMDAS process to achieve -48; alas, my calculator disagrees. It would seem that perhaps either the...
18. ### Problem on lexicographic order

Hello! How to find well ordered sets (X,<_1), (Y,<_2) such that X\times Y with lexicographic order isn't isomorphic to Y\times X with lexicographic order? Thank you!
19. ### MATLAB 2nd order nonlinear coupled differential eq

Hey Everybody, i have to do a simulation in matlab by simulating the motion of a babyboot. But my problem is that i dont know what to do. This is the link of the excercise i have to do: http://www.stanford.edu/class/me331b/documents/BabybootEOMStudent.pdf Maybe someone could help me and...