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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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
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2answers
34 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
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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
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1answer
24 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
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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
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2answers
53 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
338 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 ...
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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
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2answers
36 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
87 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
25 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
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0answers
38 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
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1answer
34 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
15 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
212 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
47 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
29 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
26 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
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1answer
26 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
21 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
27 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
12 views

Straight Line equation from determinant of a matrix

Question: det(matrix{{2, r, y}, {n, 1, 1}, {2, 1, 3}}) = 0 if the gradient or m is 4, what is the straight line equation? Steps using diagonals method: ...
0
votes
0answers
115 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
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0answers
37 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
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1answer
37 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
186 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.
0
votes
0answers
7 views

Solving an equation using Find Funtion-Matchcad

Hi I am trying to solve an equation in matchcad using Find funtion, but it gives me an error. Can some one help me on this. Below is the equation
0
votes
3answers
51 views

Systems of equations [solved]

I'm currently working on a decision problem, and for some reason I am struggling with a system of equations, which should be the easiest part of the problem. The correct answers are [(2,11),(1,11)] ...
0
votes
0answers
23 views

Solving large non-linear polynomial equation system

I have a 2 order equation system of 7 unknowns. It is constructed as this: F1=0,F2=0,F3=0...F7=0 of which F1=f1*f2,F2=f3*f4... And f1=a1*p1+a2*p2+a3*p3+a4*p4+a5*p5+a6*p6+a7*p7 a1~a7 are known ...
0
votes
0answers
19 views

Finding all values of a linear system with more than one value

I am working on some problems for practice and I have come across a type of problem I hadn't seen before. The question asks to find the values of $t$ and $s$, such that the system has (unique, ...
3
votes
1answer
35 views

Finding the zeroes of a function

How do I find the zeroes of the function $S$, below? I want to find the zeroes of $$S = 4\psi_2$$ Where $$\dot{\psi}_1=2\psi_2$$ $$\dot{\psi}_2=-2\psi_1$$ and I have that(from below) ...
2
votes
1answer
31 views

Modular Cubic Formula

What would be the process of solving a modular cubic equation? Eg. $$ax^3+bx^2+cx+d=0\pmod n$$ In the case that I was given, $d$ is a (very) large number, so rational root theorem isn't a viable ...
4
votes
1answer
85 views

What are the integer solutions of the system $a^2+b^2=c^2$, $a^3+b^3+c^3=d^3$?

How to solve these equations to find the integer numbers (a, b, c, and d)? $$a^2+b^2=c^2\tag{1}$$ $$a^3+b^3+c^3=d^3\tag{2}$$ I know one of solutions which is $a=3, b=4, c=5, ...
1
vote
0answers
21 views

Autonomous system

Exercise 2. Consider the autonomous system $$\left\{\begin{array}{l} u_{1}'=u_{2}\\ u_{2}'=-u_{2}^{3}-u_{1} \end{array}\right.$$ and the function $V(u_{1}, u_{2})$ in $\mathbb{R}^{2}$ given by ...
5
votes
4answers
885 views

A Five Equations problem?

If, $$\begin{align*} y+u+x+v&=0\\ z+y+v+u&=1\\ x+y+z+u&=5\\ z+u+v+x&=2\\ v+x+y+z&=4\,, \end{align*}$$ What is the value of $xyzuv$?
1
vote
1answer
19 views

Solving for x (Modular Arithmetic)

Solving systems of equations with Modular Arithmetic can be complex, especially with the following equations: $$(a_0x+{a_0}^2)^e \equiv C_0\;(mod\;n)$$ $$(a_1x+{a_1}^2)^e \equiv C_1\;(mod\;n)$$ My ...
1
vote
3answers
48 views

Determinant as a number that tells if a system has solution or not

There are many ways to define and interpret determinants. The one I'm more intersted rigth now is the one that better describes its name: a number that can determinate if a system of linear equations ...
0
votes
3answers
36 views

Complex numbers in my system of equations

This is for an optimization problem? I haven't dealt with complex numbers(although I know the eigenvalues are going to give me a neutral circular node) $\begin{bmatrix}-\sqrt{2}i & 2\\ -2 & ...
0
votes
1answer
19 views

Linear Equations over $\{0,1\}$ with addition considered over $\mathbb Z$

Is there any way to solve a system of linear equations with both the coefficients and variables coming from $\{0,1\}$ but where addition is considered over the non-negative integers, not ...
1
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2answers
35 views

Take two pieces of wood one 84 inches the other 74 inches. Need to cut equal amounts of 12.5 inches and 7.75 inches. How to solve?

So the system would look something like this. 74" < 12.5x + 7.75y < 84" 60" < 12.5w + 7.75z < 74" y + z = x + w where x, y, w, z are natural numbers ...
3
votes
1answer
30 views

Periodic solutions of this systems

I need to prove that the system of differential equations $$ \dot x = y \\ \dot y = 1+x^2-(1-x)y $$ doesn't contain periodic solutions. I know the Bendixon criteria (that is to have div no sign ...
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votes
1answer
36 views

If a linear ODE system has a solution that tends to zero, it also has an unbounded solution

$a:[0,\infty)\to \mathbb{R}$ is a continous and bounded and $$x'(t)\ =\left(\begin{matrix}0&1\\-a(t)&0\end{matrix}\right) \ x(t)$$ has a non-zero solution like $y(t)$ such that $\lim_{t ...
3
votes
1answer
94 views

Quadratic equation, math olympiad question

So this is a 9-10th grade, math olympiad problem I found. Define the parabola $y=ax^2+bx+c$ such that $a,b,c$ are positive integers. Suppose that the roots of the quadratic equation $ax^2+bx+c=0$ are ...
0
votes
1answer
33 views

Plotting the phase portrait of $\dot x = x(x-y)$ and $\dot y = y(2x-y)$

I am trying to plot the phase portrait of $\dot x = x(x-y)$ and $\dot y = y(2x-y)$ Now I have already found the fixed points of the system, (0,0). I have also found the Jacobian of (x,y) and when ...
1
vote
3answers
46 views

How would one solve this system

$$12x^2=6z\\2y=-z\\6x-y=7$$ It's been many years since I've dealt with system equations, and now find myself in need to solve them. I am not quite sure what to do; I am interested in finding $x$ and ...
1
vote
1answer
29 views

Modular Arithmetic with 2 Different Moduli

How can I go about solving the following 2 linear congruences? $x \equiv 2 \pmod 7$ $x \equiv 5 \pmod {11}$ How am I supposed to work with these if they are different moduli? Any help on how to do ...