This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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22 views

Analytical Case Differentiation

is there a analytical way for case differentiation? In my case a MonteCarlo Simulation calculates a system of equations. Parameters can randomly change so that the underlied mathematical condition ...
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2answers
40 views

Simultaneous trigometric equation with three angles; how to find two of them?

\begin{cases} P\cos a + Q\cos b + F\cos c = 0 \\ P\sin a + Q\sin b + F\sin c = W \end{cases} I am trying to find $a$ and $b$. My initial attempt was using the identity $\sin a = \sqrt{1 - \cos^2 a}...
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1answer
43 views

Use elimination to solve this system for $x(t)$, $y(t)$, and $z(t)$

So I took linear algebra a few years ago, so I'm a little rusty on how to do ref and rref, but I imagine it can be used to solve this. I just don't understand my output. Here is the system of ...
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0answers
35 views

How do I solve system of linear equations with 4 variables?

We have system of linear equations $A\vec{x}=b$ : $A=\begin{pmatrix} 2& 1& -1& -1& 1& \\ 1& -1& 1& 1& -2& \\ 3& 0& 0& 0& -1& \\ ...
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1answer
38 views

Finding y(t) as the solution of x' = Ax

If I have a matrix A = \begin{bmatrix}2&0\\0&3\end{bmatrix} and I am trying to find the solution y(t) to x' = Ax (Solution: x(t) = x(t), y(t)), how should I go about it? I have an initial ...
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1answer
35 views

How to calculate the transfer function from a group of equations below?

The group of equations below describe the relationship of variables from a circuit(C stands for capicator, L is for inductor etc.). And the equation at the bottom shows how the transfer function is ...
3
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2answers
69 views

Solve this system of equations using elimination for $x(t)$ and $y(t)$

I'm taking an online Differential Equations class and don't understand how to solve this system of equations using elimination. I tried the typical algebraic method but am running into trouble: ...
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0answers
33 views

Solving for $G(x,y)$ in a Gradient System (Differential Equations)

If I'm given the following, how would I solve for $G(x,y)$? $$\begin{align}\frac{dx}{dt}&=y^2-\cos x\\ \frac{dy}{dt}&=2xy-\sin y\end{align}$$ I know $x'$ is equal to the partial of $G$ with ...
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0answers
8 views

Large sparse matrix system of linear equations: finding one particular variable from the solution vector

I have an approximately $10000$ by $10000$ matrix with less than $1$% of non-zero elements. Also I don't need to find full solution vector, but only one particular variable from it. Any hints on how ...
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1answer
23 views

Eliminate a parameterization from system of equations

Let $x(t) = x_0 e^{\lambda_1t} $, $y(t) = y_0 e^{\lambda_2t} $ A book I am reading has performed the following change to remove the parameter $t$: Let $y = cx^{\lambda_2 / \lambda_1}$ where $c = \...
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2answers
48 views

Solving a feasible system of linear equations using Linear Programming

I am wondering if one could solve a feasible system of linear equations using a Linear programming approach, instead of standard linear algebra techniques such as gaussian elimination. For instance, ...
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23 views

Solving A System Of ODE's On MAPLE 17

I Have the velocity fields for two vortices that are located at two different points ${\bf{x_1}}(x_1,y_1)$, ${\bf{x_2}}(x_2,y_2)$ $\vec{V_1} = (u_1,v_1) = \frac{\Gamma_1}{2\pi}\frac{1}{(x-x_1)^2 + (...
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1answer
13 views

Solving Problems using Simultaneous Equations

Suzuki and Amin scored s and m marks, respectively , in a test. Their total score is 156 marks.If twice of Amin's score is 57 marks more than Suili's score,find Suili's score
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2answers
18 views

Variable System of Equation

Suppose we have three systems of three linear equations $E_1$, $E_2$ and $E_3$ such that $$aE_1+bE_2=E_3$$ and $$cE_2+dE_3=E_1$$ where $a$ and $b$ are non-zero constants. Express $c$ and $d$ in terms ...
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1answer
44 views

How to solve system of equations containing summation over variable to solve for?

How do we solve for $\pi_i$ in the following? $$\pi_i=\frac{\sum\limits_j N_{i,j}}{\sum\limits_j\left( \ell_{i,j} \frac{\sum\limits_k N_{k,j}}{\sum\limits_k \ell_{k,j} \pi_k}\right)}\qquad\forall i,\...
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5answers
65 views

How to verify that one of equations in a polynomial system is redundant?

I know that system of polynomial equations $$ p_1(x_1,\dots,x_n)=0,..., p_N(x_1,\dots,x_n)=0 $$ has infinitely many solutions. I computed some of them numerically and notices that they always satisfy ...
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0answers
16 views

Solving this system of equations of reciprocals?

Following on from How to solve this system of equations containing reciprocals?, my system of equations has become: $p_i = \frac{b_i}{b_i + l_i+mr_i}$ where $i\in\mathbb{Z}$ $b_i, l_i, r_i >0$ ...
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0answers
33 views

Isolating roots of polynomial system

I would like to isolate the regions which contain the roots of a system of two bivariate cubic polynomials. I thought I would project the solutions onto $x$ and $y$ axis by means of resultant ...
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2answers
55 views

Can the system of equations be extracted from its solution?

While I was solving the secondary school exam of 2014 I came across a question that states: After solving those equations: $a_{1}x + b_{1}y = c_{1}$ and $a_{2}x + b_{2}y = c_{2}$, we found that x = $\...
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1answer
20 views

About Duffing equation

Is there a relation between Duffing equation and Van der Pol equation? My second question is what is the application(s) of stochastic Duffing equn. in practice ?
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2answers
33 views

Basic algebra question. Find W in a system with 3 other unkowns and 2 equations.

I suspect this is a ratter dumb question, but I just want to be sure. I need to find W in the following equation: $$W=\frac{3}{2}x+\frac{6}{5}y+\frac{2}{7}z$$ And the only thing I know is: $$5=3x+6y+...
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1answer
94 views

I can't solve this Algebra 1 equation: For how long did she run?

Before going to school, Eudora ran from her home to a secret laboratory at an average speed of 12 km/h. Since she was running late, she then took one of her jetpacks and flew to her school at an ...
2
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1answer
32 views

Finding the two points on a heart curve which have maximal distance between them

How do I find two points on this curve that have maximal distance between them? I tried to use Lagrange multiplier to solve this, but solve equations is diffcult.
2
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1answer
21 views

How to determine the number of free variables in a nonlinear system?

Consider the system of equations $$ \begin{align} a_1 b_2 &= c_1 \\ a_1 b_3 &= c_2 \\ a_2 b_1 &= c_3 \\ a_2 b_3 &= c_4 \\ a_3 b_1 &= c_5 \\ a_3 b_2 &= c_6 \\ \end{align} $$ ...
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1answer
15 views

Free variable located on a pivot position of a matrix?

I'm really confused here. I'm having trouble seeing why is $ x_1 $ a free variable instead of a zero-valued variable, while finding the null space of the following matrix. I shall post my progress: ...
4
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1answer
31 views

Systems of ODE to High-Order converstion: Why?

I am the TA for a course in ODE, and one of my students asked me a question yesterday: why in the world do we bother with converting between (constant-coefficient) systems and higher-order ODE? I ...
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0answers
32 views

Classifying of differential equations

this is exercise 1.3 and 1.6 from Geralds book (which is free: http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf). The exercises I'm about to present are short and very related (I think), that'...
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2answers
60 views

What functions $u(x)$ and $v(x)$ satisfy $u(x) = v'(x)$ and $u'(x) = v(x)$?

I recently came across a problem in a calculus textbook which involved functions satisfying the relation $u(x) = v'(x)$ and $u'(x) = v(x)$. The problem didn't list any specific functions that for ...
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1answer
27 views

Determine whether or not( (x+y+z)==(p+q+r) and E1==E2 and (x!=p or y!=q or z!=r))

there are two number E1 and E2 $$E1=Ax + By + Cz \quad\mbox{and}\quad E2=Ap + Bq + Cr$$ Value of $A,B,C$ are different and positive integers. Value of $x,y,z,p,q,r$ may be same and they are ...
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0answers
8 views

Eliminating dependent variables

consider $Ax=b$ in which $A$ is a symmetric matrix of size $m$ and rank $m-r$. On the other hand, $B_{r\times m}x=0$ provides $r$ equations by using which the system of equations can be reduced to a ...
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1answer
32 views

Trouble manipulating equations

Can someone please help me find the values of $a$, $b$ and $e$? Thank you so much! 1) $\frac{1}{2}e - 4a = 0$ 2) $\frac{1}{2}e - 2b = 0$ 3) $\frac{3}{8}(1 + a) + \frac{1}{8}(1 + b) - 2e = 0$
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2answers
51 views

The only natural number $x$ for which $x+\sqrt{-2}$ is a cube in $\mathbb{Z}[\sqrt{-2}]$ is $x=5$

Let $A = \mathbb{Z}[\sqrt{-2}]= \{a+b\sqrt{-2} \ : a, b \in \mathbb{Z}\}$. Show that the only natural number $x$ for which $x+\sqrt{-2}$ is a cube in $A$ is $x=5$. So I have to show that there ...
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2answers
55 views

$a$,$b$ and $c$ are roots of the equation $x^3-x^2-x-1=0$

The roots of the equation $x^3-x^2-x-1=0$ are $a$,$b$ and $c$. if $n \gt 21 $ and $n \in \mathbb{N}$ The find the possible values of $$E=\frac{a^n-b^n}{a-b}+\frac{b^n-c^n}{b-c}+\frac{c^n-a^n}{c-a}$$ ...
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0answers
12 views

Finding eigenvalues of system of PDEs.

I have the following system of PDEs for $\phi(x,t)$: $$ \phi_{xx} = -\lambda \phi \\ \phi_t = 4\phi_{xxx}, $$ with $\lim_{|x|\to \infty } |\phi(x,t)|= 0$. I need to find the (possibly complex) ...
1
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1answer
22 views

How to explain some gaps in understanding of the following interpretation of a given proof?

I've been teaching myself linear algebra, and have come to the point where I'm studying the theorem which states that RREF matrices are always unique. I found this proof, but I'm not sure if my ...
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0answers
19 views

Why does biconjugate gradient (BiCG) work for nonsymmetric matrices?

After looking through the derivation of CG, I understand why it requires the coefficient matrix $A$ to be symmetric, since the property is used to produce a short recurrence relation for the ...
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1answer
26 views

Show that two ways to sum the entries of an $n\times n$ array yield the same

Let $A = (a_{ij})$ be a matrix. I am looking for an algebraic proof that $$ \sum_{\sigma, \tau \in S_k} \mbox{sgn}(\sigma\circ\tau) a_{1\sigma(1)}a_{2\sigma(2)}\cdots a_{n\sigma(n)}a_{1\tau(1)}a_{2\...
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2answers
76 views

Geometrical interpretation of solving a $3 \times 3$ system of equations

Solve the following system of equations and give a geometrical interpretation of the result. \begin{align*} x + y + z &= 6\\ 2x + y − 3z &= -5\\ 4x − 5y + z &= −3 \end{align*} I know that ...
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3answers
30 views

Find $\frac{y}{x}$ from $3x + 3y = yt = xt + 2.5x$

I need to find the ratio of $$\frac{y}{x}$$ If given that $$3x + 3y = yt = xt + 2.5x$$ So what I tried is: $$t = \frac{3x + 3y}{y}$$ And then put it in the equation $$\frac{x(3x + 3y)}{y} + 2.5x ...
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2answers
41 views

It is known that $y = ax^2 + bx^3$; when $x = 2$, $y = 5.6$, and when $x = 3$, $y = 25$. Find the values of a and b.

$$5.6 = 4a + 8b$$ $$25 = 9a + 27b$$ $$5.6 - 25 = ( 4a + 8b ) - ( 9a - 27b )$$ $$-19.4 = -5a - 19b$$ I'm stuck at that point. $$a = -1.36$$ $$b = 1.38$$
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2answers
36 views

How do I give an algebraic specification for the range of a matrix?

I am given the following $3 \times 3$ matrix: $$\begin{bmatrix} 1 & 2 & 3 \\ 1 & 3 & 1 \\ 2 & 2 & 10 \end{bmatrix} .$$ Once reduced, I get the following augmented matrix: $$\...
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2answers
49 views

Resolve $ \frac{120}{x+y} + \frac{60}{x-y} = 6;\,\frac{80}{x+y} + \frac{100}{x-y} = 7$

I want to resolve this system of equations: $$\begin{cases} \frac{120}{x+y} + \frac{60}{x-y} = 6 \\\frac{80}{x+y} + \frac{100}{x-y} = 7\end{cases}$$ I came to equations like $$x - \frac{10x}{x-y} + ...
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0answers
19 views

Is it possible to solve this system of nonhomogeneous DE?

I am following this ARTICLE on solving the differential equations. Take a closer look at page 580, chapter "11.7 Nonhomogeneous Linear Systems" - Theorem 23. Follwing this work, brought me to the ...
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1answer
55 views

Simplifying a complex trigonometric expression

Context: In a previous question , I've stated I'm making a program that will be used for calculating stuff with Statics of a particle. I've come across another scenario in which there's three forces ...
4
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2answers
133 views

Radius of a largest circle inscribed under $y=\frac{1}{(1+x^2)^n}$, closed form

The curve $y=\frac{1}{1+x^2}$ has an obvious connection to circles, because it's the derivative of the arctangent function. Besides, if we inscribe a circle under it, its radius is exactly $R=\frac{1}...
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1answer
106 views

How to find dispersion relation for a system of linear ODEs

I am trying to find the dispersion relation for a system of linear ODEs. I can do this for a single linear PDE, for example $$u_x = u_t$$ by substituting $u = Ae^{i(kx-wt)}$, here $w = w(k)$ where $k$...
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2answers
42 views

system of equation with cosh and sinh

is there simple a way solve this system to find the unknown x and y $$cosh\frac{a+x}y=\frac{b}{y}$$ $$sinh\frac{a+x}y=tanθ$$ My attemp: dividing these equations we get $$tanh\frac{a+x}y=y\frac{...
0
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1answer
24 views

Four mutually exhaustive sets; finding the intersection of two sets. Set theory and system of equations.

In a group of 120 persons there are 80 elements of B and 40 elements of G. Further 70 persons in the group are M and the remaining are H. Then the number of elements that are both in B as well as M. ...
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0answers
27 views

System of ODEs: unstable node

For a 2x2 ODE system $\mathbf{x}' = A\mathbf{x}$, where $A$ has distinct positive eigenvalues $0<\lambda_1<\lambda_2$, and $\mathbf{x}(t) = (x_1(t),x_2(t))^T$, the origin in the $x_1 x_2$-plane ...