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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2answers
36 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
45 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
1answer
60 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
34 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
16 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
42 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
38 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
35 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
54 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
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0answers
28 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: $det(A-\lambda I)=0$ ...
1
vote
1answer
31 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 ...
1
vote
0answers
32 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
17 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
59 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
31 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
21 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
30 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
1answer
17 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
2answers
36 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
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0answers
28 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
38 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
74 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
43 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
49 views

How do I solve these four simultaneous equations?

I have been trying hard to solve these equations. There are four equations in total: $$ \begin{align*} px^{p-1} + qx^{q-1} \lambda &= 0 \\ py^{p-1} + qy^{q-1} \lambda &= 0 \\ pz^{p-1} + ...
1
vote
1answer
22 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
26 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 ...
1
vote
2answers
45 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
56 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
346 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
61 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
44 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 ...
3
votes
1answer
94 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
28 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
39 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 ...
1
vote
1answer
47 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: ...
1
vote
0answers
17 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 ...
5
votes
2answers
216 views

Can it be decidable for any polynomials to have the intersecting point?

Give system of polynomials$$P_1(x_1,x_2,\dots,x_n)=0,$$$$\vdots,$$$$P_k(x_1,x_2,\dots,x_n)=0$$ Can it be decidable for thoses polynomials to have the intersecting point ?
0
votes
1answer
51 views

Help Solving coupled linear PDEs by Separation of Variables

I would like to solve the following coupled system of linear PDEs by separation of variables, where a and b are constants: ${\partial{u}\over\partial{t}} = {b-a \over a+b}u + (b+a)^2v + ...
0
votes
1answer
38 views

Combining the duality principle and the graphical method

I am trying to minimize this linear program by combining the duality principle and the graphical method: I can't seem to find an example of how to approach this, can anyone show me how I would go ...
1
vote
1answer
33 views

Direction Field and Trajectories

I am wondering how to draw a direction field and trajectories of a system of linear equations: $$ x'= \left[ \begin{array}{ c c } 4 & -2 \\ 8 & -4 \end{array} \right] x .$$ I ...
1
vote
1answer
28 views

Converting scalar ODE to coupled system

I'm currently battling the following problem: \begin{align} u^{(iv)} (x) &= f(x)\quad\text{on }(0,1)\\ u(0) = u'(0) &= 0\\ u''(1) = u'''(1) &= 0 \end{align} which is, as I've understood, a ...
0
votes
1answer
22 views

Solving trigonometric system of equations

What are the solutions for this system of equations when $\alpha \in \mathbb{R}$ is considered a constant and $0 \leq x < 2\pi$. $$ I) \ (y - \cos x)\sin x + (\alpha - \sin x) (-\cos x) = 0$$ $$ ...
1
vote
1answer
31 views

Solving A System Of Differential Eqautions

So I'm a little unsure about how to solve this system of differential equations. I missed the first five minutes of my instructor's lecture the day we went overt this, so I feel like I didn't quite ...
0
votes
0answers
117 views

An Interesting Function

What would be the fastest method to compute Hyperfactorial Function written below F(n,r)=H(N)/H(r)*H(N-r) where r < N where H(N)=(1^1)(2^2)(3^3).....(N^N)
1
vote
0answers
38 views

Does the system of equations always have a nontrivial solution?

$f:[0,1]^2\to R_+$ is a continuous conditional density function. For $g,h\in C$ on $\{(x,y)\in [0,1]^2|x\geq y\}$, the system of equations is given by$$ \frac{\partial g}{\partial x}\leq ...
1
vote
1answer
40 views

Linearisation of a system of equations - answer check

Find all of the critical points for the following nonlinear system. $$\begin{pmatrix}\dot{y}_1 \\ \dot{y}_2\end{pmatrix}=\begin{pmatrix}-y_1+ y_2 - 2\\ y_1 -y_1y_2^2\end{pmatrix}$$ and then use ...
3
votes
2answers
190 views

Fast way to come up with solutions to $x(x-1)(x-2)(x-3)=1$?

I can solve this equation $x(x-1)(x-2)(x-3)=1$ using the usual method but I am looking for a fast analytical method to solve this. Any hints ?
3
votes
2answers
61 views

Generalized way of solving this types of equations $x^3 +y^4 =z^5$

$$x^3 +y^4 =z^5$$ How can I solve this equation.I only know trial and error method, but it's not a generalized way. Please tell me a generic way to solve this type of equation.