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.

learn more… | top users | synonyms (1)

0
votes
0answers
545 views

Coupled Differential equation of second order in matlab

I have a problem solving a system of differential equations of second order in matlab: $$ \left\{ \begin{array}{l l}\frac{d^2y}{dt^2}= \frac{-y}{(x^2+y^2)^{3/2}}\\ \frac{d^2x}{dt^2}= ...
1
vote
2answers
43 views

Laplace transform for IVP not at zero in system of differential equations

Suppose we have a system $\boldsymbol X'=\boldsymbol A\boldsymbol X$. Let's denote the laplace transform of a vector $\boldsymbol Y$ as $\mathscr L\{\boldsymbol Y(t)\}(s)=\boldsymbol y(s)$. If we ...
1
vote
0answers
45 views

Solve this equation

I have the conditions $$1 = e^{\alpha-1} \sum_{n=1}^M e^{\beta E_n + \gamma N_n} $$ $$\langle E \rangle = e^{\alpha-1} \sum_{n=1}^M E_n e^{\beta E_n + \gamma N_n} $$ $$\langle N \rangle = e^{\alpha-1} ...
3
votes
4answers
189 views

System of congruence equations

I have a system of congruence eqs $$ \begin{cases} x \equiv 14 \pmod{98} \\ x \equiv 1 \pmod{28} \end{cases} $$ I have calculated $\text{gcd}(98,28) = 14$. I can from the congruence eqs get $x = ...
0
votes
0answers
38 views

Fastest way to solve specified system of nonlinear equations

I have a following system of equations \begin{equation} \begin{aligned} \sum\limits_{i = 1}^3 g_i V_{i, x} & = (\sum\limits_{i = 1}^3 g_i n_{i, x})t + P_x \\ \sum\limits_{i = 1}^3 g_i ...
0
votes
1answer
277 views

Solve nolinear system of equaion with c/c++ [closed]

My system of equation is like this: (x-a1)^2 + (y-b1)^2 = c1 (x-a2)^2 + (y-b2)^2 = c2 I know it is simple using matlab: ...
1
vote
1answer
44 views

Finding solutions of system of differential equations with eigenvectors

I was trying to solve this system of differential equations: $$\frac{dx}{dt}=3x-y-z$$ $$\frac{dy}{dt}=x+y-z$$ $$\frac{dz}{dt}=x-y+z$$ I found the eigenvalues: $\lambda_1=1,\lambda_2=2$. The ...
1
vote
0answers
34 views

Non-linear system of exponential equations with 2 boundary conditions: $p(y_m)=p_m$ and $\frac{dp(y)}{dy}$

I have this equation: $$ p(y) = -\left(e^{-\tfrac{K_{py}zy}{p_u+c e}}-1\right)\left(p_u+c e^1\right)-c\left(1-e^{-y}\right)^d\left(e^1-e^{1-y}\right) $$ The two unknowns are $c$ and $d$ and the system ...
2
votes
2answers
34 views

When does a linear system have infinitely many solutions, yet some of them don't depend on the others?

Consider this system: $$ \begin{cases} w + x + y + z = 1 \\ w + x + y + 2z = 2 \end{cases} $$ Its solution set is $\{z = 1,\, y= -w - x \;|\; w,\,x \in \mathbb{R}\}$. So, $z$ is "fixed," in a sense. ...
0
votes
1answer
20 views

How were these two equations rearranged to this from?

$$f(x)=F(x)+G(x)$$ $$g(x)=-cF(x)+cG(x)$$ To: $$F(x)= \frac{1}{2}f(x)-\frac{1}{2c}g(x)$$ $$G(x)= \frac{1}{2}f(x)+\frac{1}{2c}g(x)$$ I can kind of see the relationship between the equations but if ...
1
vote
1answer
26 views

Determine parameter so that the absolute value of real solution of the equation is larger than the modulo of complex solution

Given the equation: $$x^3+x+\lambda=0$$ determine real parameter $\lambda$ so that the real solution is greater by absolute value than modulo of the complex solutions. My attempt: Let $x_1$ be the ...
0
votes
1answer
62 views

Roots of an equation using Maple

I am using Maple to find the roots of a non-linear equation in one variable. When I solve the equation, I get only 2 negative roots whereas if I plot the graph of the function, it also shows that the ...
0
votes
1answer
33 views

Building an nth order ODE in Maple (or Matlab)

The question is simple: given a system of ODEs, how can one construct the equivalent nth order ODE in Maple? In my case I have $$ \begin{cases} y''(t)+x'(t)+x(t)=f(t)\\ y''(t)+z''(t)+z'(t)+z(t)=0\\ ...
0
votes
1answer
41 views

Finding initial conditions for which solutions to IVP are periodic

I have an initial value problem $\mathbf x'=A\mathbf x$ $$A = \begin{pmatrix} 1 &1 &0 &0 \\ 3& -1 &0 &0 \\ 0 &0 &0 &-2 \\ 0 &0 &2 &0 ...
2
votes
0answers
66 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 ...
3
votes
1answer
106 views

Linear system for which the solution space is spanned by the given vectors

Make a system with $3$ equations and $3$ unknowns of which the solution space $V$ is spanned by the column vectors: $$\begin{bmatrix} 1 \\0 \\-1\end{bmatrix},\quad \begin{bmatrix}1 \\3\\ ...
0
votes
1answer
24 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 ...
0
votes
0answers
24 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
38 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
55 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
88 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
37 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
18 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
48 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
51 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
37 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
57 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:
0
votes
1answer
55 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
104 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
53 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
62 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
73 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
38 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
33 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
16 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
32 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
21 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
41 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 ? ...
3
votes
1answer
43 views

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

Given this problem Restrictions on $x$ any are that $x\in[0,\pi]$ , $y\in[0,\pi]$ I have $f_x=-(\cos y)({\sin(2x+y))}--------*$ $f_y=-(\cos x)(\sin x+2y)-----------**$ So from $*$ I get either ...
0
votes
1answer
44 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
76 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
46 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
55 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
23 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
34 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
54 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
76 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
360 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
vote
2answers
244 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
111 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: $$x+y+z=6$$