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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2
votes
0answers
45 views

Study of a system of differential equations

I'm asked to study everything that is possible to know about the sytem$$\begin{cases}x'=x^2-y^2\\y'=2xy\\z'=-z\end{cases}$$ My questions here is, how much can be know about it?, how do I know I ...
-6
votes
3answers
68 views

Is it possible to find [on hold]

If $$\frac {(a-b)(c-a)}{(b-c)(d-c)}=\frac {2012}{2013}$$ then find the value of $\dfrac {(a-c)(b-d)}{(a-b)(c-d)}$ in terms of numbers Note: $a,b,c,d$ are real numbers
1
vote
0answers
19 views

Prove that if (0,0) is a simple critical point of a quasi linear system , then it is necessarily isolated. [on hold]

Consider the system \begin{cases} \frac{dx}{dt}=a_{1}x+b_{1}y+f(x,y) \\ \frac{dy}{dt}=a_{2}x+b_{2}y+g(x,y) \end{cases} it will be assume that $det \begin{pmatrix}a_{1} & b_{1} \\ a_{2} & ...
0
votes
1answer
18 views

Help solving system of linear equations.

In the process of running through an algorithm, I have derived the following systems of equations: i) $1/3 + 1/3x_1 + 1/3 x_6 = x_5$ ii) $1/2 + 1/4 x_6 = x_1$ iii) $1/2 + 1/2 x_5 = x_6$ I've tried ...
2
votes
1answer
41 views

Is there analytical solution to $x^{a+1} + x^{a} = c$ with $0<a<1$?

How to solve the nonlinear equation of type $x^{a+1} + x^{a} = c$ with $0<a<1$ and $c>0$? Sorry, I don't know which tag is appropriate.
0
votes
0answers
14 views

On Farkas's Lemma and Existence of a particular solution

This is a real life problem. I have a matrix $A$ which is $m\times n$. I want to check for the conditions on the existence a vector $x\in\mathbb{R}^n$ such that $A x \geq 0$. The Farkas's Lemma, as I ...
1
vote
2answers
34 views

Find $\log_c{x}$ if $\log_a{x} = p$, $\log_b{x} = q$, and $\log_{abc} {x} = r$.

Given that $\log_a{x} = p$, $\log_b{x} = q$, and $\log_{abc} {x} = r$, find the value of $\log_c{x}$.
0
votes
1answer
37 views

Solving a simple systems of equations

Update: 1) As @Amzoti mentioned, I made a mistake in the mathematica code. There should be spaces between x, y and z. So now the following code works: ...
2
votes
0answers
47 views

Stability of nonlinear system of PDE's

Let's assume system $$ \tag 1 \frac{\partial \mu}{\partial t} = \gamma (\mathbf B \cdot \mathbf E), $$ $$ \tag 2 [\nabla \times \mathbf E] = -\frac{\partial \mathbf B}{\partial t}, $$ $$ \tag 3 ...
0
votes
3answers
30 views

Find couples of complex numbers

I found this exercise, given: $$u=|z|+|u|$$ and $$z=|u|+1$$ (it is a system I don't how to write it in latex from) I have to find the couples of complex numbers $u,z$ that comes from the two equation. ...
0
votes
0answers
14 views

Find a matrix and a vector using partial derivative and system of matrices.

Let $f(x)$:=[$f_1(x),...,f_d(x)]^T$ and suppose that |$\frac{\partial^2 f_i(x)}{\partial x_j \partial x_k}|$$\le$K for all $i,j,k$=1,...,d and $x\in\Re^2$. Show how to define an $dxd$ matrix $J(y)$ ...
0
votes
2answers
40 views

Solve system of equations

Are there any good resources for solving systems of equations out there? I tried to put this into wolfram alpha, but it doesn´t seem to work: ...
3
votes
1answer
30 views

Polynomial curve fit

Well I have a 2 (or 3) data points - and some extra limits - and a polynom needs to be fitted through those points (exactly). The polynom needs to be of the smallest order, and not a least square, it ...
2
votes
3answers
33 views

Prove that one of x,y,z is smaller than 3 and one is bigger than 5 if…

If $x+y+z=12$ and $x^2+y^2+z^2=54$ then prove that one has to be smaller or equal to 3 and one has to be bigger or equal than 5. So I got that $xy+yz+zx=45$ and with that I had a function with x,y,z ...
0
votes
4answers
49 views

Solve system of equations

$$\sin(x+y)+1.6x=0$$ $$x^2+y^2=-1$$ Can this system be solved? Please help me with it. I managed to make graphs of it but can't get it solved without graph. Graph:
1
vote
0answers
22 views

Solving a homogeneous linear system of differential equations: no complex eigenvectors?

I have to solve the following equation by diagonalization. $ X' = \begin{bmatrix}1 & 1\\1 & -1\end{bmatrix} X$ I was able to determine the complex eigenvalue roots: $det(A-\lambda I)=0$ ...
0
votes
1answer
38 views

Three positive real numbers [closed]

Let $a$,$b$,$c$ be positive real numbers such that $abc$ is not equal to $1$ and $$ [(ab)^2]=[(bc)^4]=[(ca)^k]=abc $$ Then $k$ is equal to
1
vote
1answer
26 views

Solve equation with unknown in exponents

This is in continuation of this but not related to it completely. I am interested in finding a solution to the equation: $m' = m - \sum \limits_{j=1}^{m} (1 - d_{O_j}/n)^k$. where $m,m',n$ and ...
0
votes
0answers
20 views

Solving over-identified model in Mathematica

I am having trouble with using the "Solve" function for an over identified model in Mathematica. For a just identified model, where I have as many equations as I do unknowns the "Solve" function ...
1
vote
0answers
26 views

General solution for system of differential equations with only one eigenvalue

If I'm given a system of equation of the form $$\begin{cases} \frac{dx}{dt}= ax+by \\ \frac{dx}{dt}= cx+ey\end{cases}$$ I get the general solution finding the eigenvalues and eigenvectors of the ...
0
votes
2answers
12 views

All the solutions for this system 5x+33y = 6 (mod 13) and 7x + 2y = 9 (mod 13)

I want all the solutions for this system. 5x + 3y = 6 (mod 13) and 7x + 2y = 9 (mod 13)... Thanks
3
votes
1answer
49 views

Find all positive solutions of the system of equations

Find all positive solutions of the system of equations $x_1+x_2=(x_3)^2$ , $x_2+x_3=(x_4)^2$ , $x_3+x_4=(x_5)^2$ , $x_4+x_5=(x_1)^2$ , $x_5+x_1=(x_2)^2$ What i have done : ...
-2
votes
2answers
25 views

Find sum of arithmetic progression [closed]

I have been given that A4(the fourth element) is equal to 5 and I have to find the sum of the first 7 elements. I tried using system to find A1(the first element) or d(the difference) but I was unable ...
0
votes
2answers
20 views

System of Equations Given One Equation

7=3x+2y-z How many more equations would you need to solve x, y, and z? In which variables can the additional equations be? Give examples of equations that would help solve these variables. (Hint: ...
0
votes
0answers
15 views

Lines where the tangent to the trajectories is $0$ or $\pm\infty$

I have the following system of equations: $\def\b{\begin{pmatrix}}\def\e{\end{pmatrix}}$ $\b\dot{y}_1 \\ \dot{y}_2\e=\b2&0\\3&-1\e\b y_1\\ y_2 \e$ and I need to find the equation of straight ...
1
vote
0answers
23 views

Chinese Remainder Problem with three equations

Let's consider: $$*\begin{cases} 7x \equiv 2 \mod 5\\ 3x \equiv 2 \mod 4 \\ 5x \equiv 2 \mod 6 \end{cases}$$
0
votes
0answers
30 views

Linear System of Equations with Equality Constraint

I'm trying to solve a simple system of linear equations (4 equations, 4 unknowns) using matrix calculations: $$\begin{pmatrix} ...
0
votes
1answer
14 views

Intuition: Mapping linear equation to axes

Can someone give an intuition of how linear equations in two variable are mapped to a 2-D plots in the forms of lines ? And why are the axes perpendicular ? I mean how come someone come with the idea ...
0
votes
0answers
13 views

Scientific Workplace-Solving system of equations

I'm using mathematical package scientific workplace to solve a system of simultaneous solutions with 7 unknowns and 7 equations. I'm using Compute-> solve->numeric but unfortunately its giving me ...
0
votes
2answers
27 views

How to solve these $ 2x + 4y + 3x^{2} + 4xy =0$ and $ 4x + 8y + 2x^{2} + 4y^{3}$ = $0 $

I need to solve these two equations . $ 2x + 4y + 3x^{2} + 4xy =0$ $ 4x + 8y + 2x^{2} + 4y^{3}$ = $0 $ I have added them , subtracted them . Nothing is helping here . Can anyone give hints ? ...
1
vote
0answers
24 views

My attempt regarding finding critical ponts of $(cosx)(cosy)(cos(x+y))$

Given this problem Restrictions on x any are that x $\in$ [0,$\pi$] , y $\in$ [0,$\pi$] i have $f_x$ = $-(cosy)({sin(2x+y))}$ -------- * $f_y$ =$-(cosx) (sin x+2y) $ -----------** So from * i ...
0
votes
1answer
30 views

Function Of Any Line?

If I were to scribble a line of varying curves into a sheet of paper and for each value of X there was only a single value of Y, how can I go about finding the function for such a line in a way that ...
0
votes
1answer
68 views

The values of $k$ for which $ \log(2x) \leq kx \leq e^{x/2}$ for all $x > 0 $

So I'm trying to solve a system of equations and I checked some other guys solution and he divides the function by the derivate, like so: $f(x)/f'(x)$. Find the values of the real constant $k$ for ...
1
vote
2answers
32 views

Solving equation-systems so it's understandable by an 11 year old

I'm trying to help my little brother with this math homework. The question: You have three numbers. The sum of these numbers are $7.2$. The second number is twice as large as the first one. The third ...
1
vote
0answers
35 views

Stuck trying to solve these equations

I have been trying hard to solve these equations .There are 4 equations in total $px^{p-1} + qx^{q-1}\lambda = 0$ $py^{p-1} + qy^{q-1}\lambda = 0$ $pz^{p-1} + qz^{q-1}\lambda = 0$ $x^{q} + y^{q} ...
1
vote
1answer
21 views

Non-linear system with all trajectories converging on the line $x=0$, rather than $(2,0)$?

I have the following nonlinear system: $$\begin{pmatrix}\dot{y}_1\\\dot{y}_2\end{pmatrix}=\begin{pmatrix}2y_1\\y_1^2\end{pmatrix}$$ Which I set up to $F=\dot{y}$ Giving the jacobian of ...
0
votes
1answer
22 views

Node: Type, Stability, Slope at origin, Trajectories. Linear system.

I have a system of equations: $$\begin{pmatrix}\dot{y}_1\\\dot{y}_2\end{pmatrix}=\begin{pmatrix}2&0\\4&-1\end{pmatrix}\begin{pmatrix}y_1\\y_2\end{pmatrix}$$ Looking at matrix $A$ I can see a ...
2
votes
3answers
28 views

Exponential equation problem

How to solve the following equation : $2^{6-n} = n$ I have no idea of to solve it. I took logarithms on both sides. But doesn't reach at some satisfactory path. But practically i 've found n must be ...
1
vote
2answers
44 views

How to solve a coupled differential equations

I tried different ways to solve this differential equation but I did not succeed. These is the first couple ODEs I try to solve. I hope somebody can give me a hint. \begin{eqnarray} \ddot{x} + ax - ...
0
votes
2answers
52 views

Solve system of kinematics equation

I want to solve the following system for $t_1 + t_2$. $$ v_f=v_i + a(t_1-t_2) $$ $$x_f=x_i+v_i(t_1+t_2)+\frac{1}{2}a(t_1^2−t_2^2)+at_1t_2$$ I've tried solving for $t_1$ and substituting, but the ...
5
votes
3answers
333 views

Solving a simple system of equations

Given the simultaneous equations $$A\cos{(\sqrt{\lambda}\pi)} + B\sin{(\sqrt{\lambda}\pi)} = 0$$ $$A\cos{(2\sqrt{\lambda}\pi)}+B\sin{(2\sqrt{\lambda}\pi)} = 0$$ We want to show this has not trivial ...
-1
votes
4answers
60 views

How to solve these two equations $2x + y = 1/x^{2}$ , $ x +2y = 1/y^{2}$ [closed]

How do I solve the following system of two equations, two unknowns? $2x + y = 1/x^{2}$ $ x +2y = 1/y^{2}$
1
vote
2answers
25 views

Finding steady state probabilities by solving equation system

(I know that there are numerous questions on this, but my problem is in actually solving the equations, which isn't the problem in other questions.) I'm trying to figure out the steady state ...
2
votes
1answer
82 views

How find this real value $x+y+z $ if such this equation

let $x,y,z>0$ and such $$\begin{cases} \dfrac{x}{xy-z^2}=-\dfrac{1}{7}\\ \dfrac{y}{yz-x^2}=\dfrac{2}{5}\\ \dfrac{z}{zx-y^2}=-3 \end{cases}$$ show that: $$x+y+z=6$$
0
votes
2answers
24 views

Solve equation with complex numbers using a helper equation

For the last two hours I've been trying to solve this complex equation using a helper equation. But I can't work it out. $z^2 = 5-12$ $\text{Let} \space z = x + yi$ $(x+yi)^2 = 5-12i$ $x^2-y^2 + ...
1
vote
0answers
36 views

A corollary of Niven

Please proof corollary of Niven: For $a \in D\backslash R$, the equation ${t^n} = a$ has exactly $n$ solutions in $D$, all of which lie in $R\left( a \right)$, in there $R$ is a real-closed field and ...
19
votes
9answers
6k views

System of nonlinear equations that leads to cubic equation

The system of equations are: $$\begin{align}2x + 3y &= 6 + 5x\\x^2 - 2y^2 - (3x/4y) + 6xy &= 60\end{align}$$ I can solve it through substitution but it is an arduous process to reach this ...
-4
votes
0answers
21 views

Prove that the total energy of the system decrease?

Prove that the total energy of the system $$\begin{cases} U_{tt}=c^2U_{xx}-a^2U_t,&\Omega\in\Bbb R^n\\ U(0,t)=U(L,t)=0,&t\geqslant0\\ U(x,0)=f(x),U_t(x,0)=g(x),&\Omega\in\Bbb R^n ...
1
vote
1answer
27 views

How to solve a nonlinear system in Matlab without saving a function

Peace be upon you, I have a system of equations to be solved. I know that I can solve my system in Matlab like this: ...
0
votes
0answers
13 views

Region of controllability for optimal control

I have an optimal control question which yields: $x=A e^{4t}\begin{pmatrix}1\\-1\end{pmatrix}+B e^{2t}\begin{pmatrix}1\\1\end{pmatrix}+\begin{pmatrix}1\\3\end{pmatrix}u^*$ For $u^* = \pm1$ So we ...