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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47 views

Stuck with neice's homework!! Ostensibly a bearings question, but I need more to solve

My neice asked me for help with her national 5 homework. (National 5 is a new qualification in Scotland roughly equivalent to the old standard grade, so I would have thought quite easy). I have made a ...
4
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1answer
62 views

Find the product xy.

Given $$ \log (x) + \frac{\log (xy^8)}{(\log x)^2+(\log y)^2} = 2\\ \log (y) + \frac{\log \left(\frac{x^8}{y}\right)}{(\log x)^2+(\log y)^2} = 0 $$ Find the product $xy$ if both $x$ and $y$ are ...
2
votes
1answer
50 views

Existence of solution of $\frac{\partial f}{\partial t}=-\Delta f+|\nabla f|^2-R(x,t)$

When $t=t_0$, $f(x,t)=f_0(x)\in L^2(U)$. $t\in [0,t_0]$ and $U$ is a open subset of $R^n$.$R(x,t)$ is bounded and smooth about $x$ and $t$. I don't whether suitable the conditions is ,if not, please ...
2
votes
1answer
57 views

Image of a cube under the flow's action

Let's consider a system of ODEs: $$ \dot{x_{1}} = \sin{x_{2}}+x_{1}\\ \dot{x_{2}} = \cos{x_{3}}-2x_{2}+x_{1}\\ \dot{x_{3}}=\arctan{x_{1}}-x_{2}+x_{3}$$ I would like to find an image of the unit cube ...
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2answers
41 views

If there's no relation between $c_1$ and $c_2$, can I say that $c_1= r\sin \theta,c_2=r\cos \theta$?

If there's no relation between $c_1$ and $c_2$, can I say that $c_1= r\sin \theta,c_2=r\cos \theta$? In other words, does the following system in the variables $r,\theta$, always have solution? $$ ...
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0answers
25 views

Venn diagram with multiple events

$65$ kids at a school voted for their favorite ice-cream flavor. They can vote for up $2$ flavors and the choices are vanilla,chocolate,and strawberry. $10$ kids voted for strawberry, $35$ voted for ...
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2answers
40 views

Solve simultaneous equations $\log(x-2)+ \log 2=2 \log y$, $\log (x-3y+3)=0$ (Not sure of solutions in book)

Solve simultaneous equations $\log(x-2)+\log2=2\log y$, $\log(x-3y+3)=0$ (Not sure of solutions in book) My method: $\log(x-2)+\log 2-\log y^2=0 \Rightarrow \log\left(\frac{x}{y^2}\right)=0 ...
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0answers
18 views

Finding Positive and Negative Limit Sets (ω(Γ) and α(Γ))

So this problem statement says Use analytical or graphical techniques to find the positive and the negative limit sets of the orbits through the listed initial points. I have a system ...
0
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0answers
25 views

Determining Solutions to a System of Congruences

I'm having trouble finding a straight-forward answer to a simple question: When solving a system of linear congruences in two variables such as: $ax+by=e \mod m$ $cx+dy=f \mod m$ ...
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2answers
60 views

Find $a$, $b$ and $c$ that satisfy the following equations

Find all integers $a$,$b$ and $c$ that satisfy the following equations $a^2=bc+1\tag{i}$ $b^2=ac+1\tag{ii}$ I tried solving came out with following results: $(i)-(ii)$ gives $a+b+c=0$ which ...
0
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0answers
50 views

How many cows will eat the field?

Three pasture fields have areas of $\frac{10}{3}$, $10$ and $24$ acres, respectively. The fields initially are covered with grass of the same thickness and new grass grows on each at the same rate per ...
1
vote
1answer
27 views

Cahn-Hilliard equation

Is there any possibility to write the so-called Cahn-Hilliard equation: $\frac{\partial c}{\partial t}=D\nabla^2(c^3-c-\gamma\nabla^2c)$, in terms of two coupled partial differential equations ...
0
votes
1answer
50 views

Converting differential equation $x''+\sin(x)= 0$ to a system of ODEs

Show that the differential equation $x''+\sin(x)= 0$ is not structurally stable. I do not know how to covert it to a system of ode.
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0answers
11 views

A question about systems of linear equations? [duplicate]

I was wondering whether a homogeneous system of linear equations with more variables than equations always has a solution other than the trivial solution. If so do you mind explaining why.
0
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1answer
25 views

Cannot find error in solution for system of ODEs

I've spent a lot of time trying to figure out where the error is, but it has not been possible to find where the error is, unfortunately. This process of "debugging" is really tiresome, and this is ...
0
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0answers
51 views

Periodic solutions of autonomous system in polar coordinates

Let $x = r \cos θ$, $y = r \sin θ$. An autonomous system is expressed in polar coordinates: $$\frac{dr}{dt} = r(1-r)(r-2), \frac{dθ}{dt} = -1$$ (a) Find all the periodic solutions (including critical ...
0
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2answers
16 views

Reassemble a system of differential equations

Given the system of equations $\frac{dx}{dt}=-\frac{3}{2}x-\frac{5}{2}y$, $\frac{dy}{dt}=\frac{5}{2}x+\frac{3}{2}y$, how can it be converted back into the second-order ODE? I've tried to do it ...
0
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1answer
29 views

system of differential equations with initial values.

I have to slove this problem. $$x'_{(t)}=\begin{pmatrix} 1 & 2 & 2 \\ 2 & 1 & 1 \\ 2 & 2 & 1 \\ \end{pmatrix} x_{(t)} ...
0
votes
1answer
23 views

How do I interpret this notation systems of diff eq course I'm taking?

I'm a college sophomore taking differential equations and I'm having trouble understanding the notation in the part of the course involving systems of differential equations. All the notation for the ...
3
votes
1answer
88 views

Solve system of $n$ equations of the form $2x_k^3+4=x_k^2(x_{k+1}+3)$

Solve the system of $n$ equations, $n\geq2$: $$ \begin{cases} 2x_1^3+4=x_1^2(x_2+3)\\ 2x_2^3+4=x_2^2(x_3+3)\\ \qquad \vdots\\ 2x_{n-1}^3+4=x_{n-1}^2(x_n+3)\\ 2x_n^3+4=x_n^2(x_1+3)\\ \end{cases} $$ I ...
1
vote
1answer
48 views

Solvability of Perelman's $\mathcal W$ system.

How to show the system have solution ? $R_{ij}$ is ricci tensor, $R$ is scalar curvature. I feel this is complex question, because I have little knowledge about PDE. So, if it is complex, just tell me ...
0
votes
1answer
19 views

Discovering “hidden solution” in system of equations

For the system of equations $x(1-4x-y)=0$ $y(1-2y-5x)=0$, One of the solutions is $x=1/3, y=-1/3$, but I don't see how to find it. Some help would be appreciated. I'm obviously having a gap here.
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3answers
34 views

System of equations with trig functions

Can someone explain to me how to solve this system of equations for the parameters $a$, $k$ and $\phi$? I already tried solving the last equation for a and plugging it into another equation, but I ...
2
votes
3answers
48 views

is $\frac{a-b}{a+b} - \frac{c-d}{c+d}$ equal to $ \frac{a-c}{a+c}$?

I am using values out of a cross-correlation analysis and my intuition tells me that the equation in the title is true, however I would like to prove it. $$ \frac{a-b}{a+b} - \frac{c-d}{c+d} = ...
0
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0answers
17 views

How to solve a set of 3 nonlinear equations (lines in space)

I would like to calculate the following: There are 3 points in space of which the coordinates are known: $C(a,b,c), M(d,e,f), A(g,h,i)$ Each point is a starting point of a line with a certain ...
1
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1answer
23 views

A system of diferential equations solved by Laplace Transform

I have this system of diferential equations $$ \begin{cases} q'+q+i=50e^{-t}u_1(t) \\ i'+i-q=0 \end{cases}$$ $q(0)=i(0)=0$ ** $ u_1(t) $ is the Heaviside step function Solution Rewriting: $$ ...
0
votes
0answers
10 views

Coupled system of second order differential equations with variable coefficients

I am currently trying to find the solutions $\phi_1$ and $\phi_2$ of a system of coupled second order differential equations of the following form: $$ ...
0
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1answer
53 views

solve two-dimensional nonlinear system numerically

Given the system $$x' = x(1 − y^2) \\ y' = y^2(1 − x^2)$$ I can plot the trajectories according to the analysis of its fixed points, but I need help with solving it numerically. Can anyone help me ...
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votes
1answer
26 views

How can we find the possible values of 'a' in a system of linear equestion?

What is/are the possible value(s) of 'a' such that the system of linear equestion in x,y and z has a unique solution? ...
3
votes
1answer
26 views

Grade 10 system of linear equation problem

A farmer harvested $1$ section (which is $640\, acres$) of wheat and $2$ sections of barley. The total yield of grain for both areas was $99,840\, bushels$. The wheat sold for $6.35\, /bushel$ The ...
1
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1answer
43 views

MATLAB fsolve giving wrong solution

I tried to solve equations of 3 spheres using MATLAB's fsolve function, but it is giving the wrong solution. here is my MATLAB function ...
0
votes
1answer
30 views

How to resolve a set of equations when everything is cross related

First off mathematics isn't my field, so if I've made any rookie mistakes please forgive me! (also I'm not sure what tags to use) I have a set of equations that boil down to this; $s = \int Vdt$ $V ...
0
votes
1answer
19 views

Can this system of equations be solved exactly?

I have a problem which I have been able to reduce to the following vector equation: $2 \alpha \vec{f} [C_0 + C_T \ \vec{a}.\vec{f}] = - C_T \ \vec{a}$ where $\alpha, C_0$ and $ C_T$ are all ...
0
votes
0answers
12 views

Linear equalities and nonequalities over finite group

Would anyone know where I could find more information on counting the number of solutions to a system of equations involving linear equalities and nonequalities over a finite group? For example, let ...
-1
votes
2answers
49 views

How can we solve the linear system? [closed]

How can we solve the following linear system ? $$ax+by=0 \\ cx+dy\neq 0$$
0
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1answer
29 views

Draw phase portrait of this system

Consider the system: $$ \begin{cases} x'=xy\\ y'= -x^2. \end{cases} $$ I find that for this system, the line $x=0$ are a line of fixed points. I wonder how to draw the phase portrait for this system.
0
votes
1answer
26 views

Give the general solution of the $2\times 2$ inhomogeneous system of differential equations

Give the general solution of the system: $$X'(t) = \begin{pmatrix} 3 & 1 \\ 1 & 3 \end{pmatrix} X(t)+\begin{pmatrix} 2e^{2t} \\ 0 \end{pmatrix} $$ I manage to come to the general solution ...
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vote
2answers
36 views

Prove that $\alpha=\beta=\gamma$

Q. Let $x,y,z \in \Bbb R-\{0\}$ and $\alpha,\beta,\gamma \in \Bbb C$ such that $|\alpha|=|\beta|=|\gamma|=1$. If $x+y+z=0=\alpha x+\beta y+\gamma z$, then prove that $\alpha=\beta=\gamma$. My ...
0
votes
1answer
61 views

System of differential equations: where did I got wrong?

I have the system: $$x_1'=2x_1-x_2+e^{2t}\\ x_2'=4x_1+2x_2+4$$ So I searched for the homogeneous solutions and got: $$X_H=c_1e^{2t} \left(\begin{matrix} \cos 2t \\ 2\sin ...
1
vote
1answer
38 views

Why equations are called independent and dependent?

I am not sure if I am trying to know everything to detail, but why for example two equations are called independent if they have only single solution? On what they think about when they say single ...
0
votes
1answer
63 views

System of differential equations

We suppose that we have a system of differential equations $$\left\{\begin{matrix} L_1 y=0\\ L_2 y=0 \end{matrix}\right. \tag 1$$ where there order of $L_1 y$ is $n$ and the order of $L_2 y$ is ...
0
votes
1answer
14 views

Find the equation of the line for this impilcit differential

Here is the question. A set of points in this graph that satisfies the the equation of the line tangent to this curve at the point (0,4) So I started by finding the derivative But I am not ...
1
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1answer
35 views

Solving a nonlinear algebraic system representing the equilibrium of a system of ODEs

Given the following system: $$ a_1+(a_3+a_4)V-a_5WX = 0 \\ (a_7+a_4)Y-a_6WZ = 0 \\ a_2-W(a_4+a_5X+a_6Z)+(a_3+a_8)V+a_7Y = 0 \\ a_5WX-(a_3+a_8+a_4)V = 0 \\ a_6WZ-(a_7+a_4)Y = 0 $$ where $a_1$ to ...
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votes
0answers
25 views

Questions regarding the basis for the solution set of a system.

I've seen a couple of examples like this but there's a thing I don't understand. I have to determine a basis for the solution set of the system: $$x-y-7=0\\ 2x-y+7=0$$ So based on the examples, ...
1
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1answer
31 views

The Rank of the Matrix Given its Solution Space

$\quad$ Let $A$ be a $5$x$4$ matrix.There exists a vector(column) $B=[0,1,2,3,4]^{T}$ such that the solution space of $AX=B$ is $[1+2s,2+3s,3+4s,4+5s]^{T}$where $s \in \mathbb R$. Find the rank of ...
2
votes
1answer
52 views

Possible values of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ given $x+y+z=1$

Given $x,y,z$ are real numbers and $x+y+z=1$ and $x$ is not equal to $z$, if $ {1\over x} + {1\over y} + {1\over z} = m $, which of the following values of $m$ are possible? (A) 1 (B) 2 (C) 3 ...
1
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2answers
41 views

Solving Currents in Electrical Networks for Graph Theory

I need help trying to solve this question, been cracking my head for the whole week and my professor said he used an online solver but in exams we have to solve by hand! Given these 8 equations, we ...
1
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3answers
40 views
0
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1answer
20 views

Number of solutions in a system for values a and b

In general, if you are given a system with some a and b like $x + y + z = a $ $x + 2z= b$ $x + ay + z=b$ And asked to find the values a and b such that the system has no solution, infinitely many ...
0
votes
1answer
16 views

Square of a matrix as coefficients for a system of linear equations

small question I'm having a disagreement with a classmate over - it's a question in a book: Let $A$ be a square matrix $n \times n$ Prove or disprove: If the system $A\underline{x}=\underline{b}$ ...