What is Equation system: Definition and 32 Discussions
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a:
System of linear equations,
System of nonlinear equations,
System of bilinear equations,
System of polynomial equations,
System of differential equations, or a
System of difference equations
How would one go about solving this for a and b given N, E and K?
n(0) + n(1) + … + n(K) = N
n(0)*0 + n(1)*1 + … + n(K)*K = E
Where n(k) = InverseDigamma(Digamma(a+1)-b*k)-1
Summary:: equation system of complex mechanism need to be done. Lagrange Formalism could be helpfull to do it but small errors could all destroy ..
Hi everyone,
I tried to find the equation system of the joined Mechanism (4 DoF). I think there is a mistake but I am not sure where is it . I...
$\tiny{27.1}$
623
Find a general solution to the system of differential equations
$\begin{array}{llrr}\displaystyle
\textit{given}
&y'_1=\ \ y_1+2y_2\\
&y'_2=3y_1+2y_2\\
\textit{solving }
&A=\begin{pmatrix}1 &2\\3 &2\end{pmatrix}\\...
Hello,
I'm having a problem with this system. Ignore the physics.
I have the feeling it should be tremendously easy... but I can't figure it out.
I don't know how to extract it from the pdf so I'll post just the these 2 pages.
https://ufile.io/39ovq
The equations are (1.14) and (1.15), the...
Hi!
Just started with linear algebra Could someone help me with this problem?
2x_1 + x_2 - x_3 + 3x_4 - 3x_5 = 0\\
3x_1 + 2x_2 + x_3 + 2x_4 + 2x_5 = 0\\
-4x_1 + 3x_2 + 2x_3 + x_4 - 4x_5 = 0
(Sorry, I don't know how to do these big brackets for equation systems in Latex.)
So it's a...
Homework Statement
Okay, this one is a bit big, and I'm attempting a translation, so I'm going to post a TL;DR version at the bottom just to be sure. Anyway, here goes:
While doing an experiment, we write down the values of a physical/natural size y, for various values of a physical/natural...
I wasn't sure into which category I should post this, so feel free to move it into a more appropriate place.
As part of my work I'm solving a system of nonlinear equations, of a usual form:
$$\vec{F}(\vec{X})=\begin{pmatrix}F_1(X_1, X_2, \cdots X_N) \\ F_2(\cdots) \\ \vdots \\...
Homework Statement
I'll try to be as clear as possible but this exercise is in portuguese and this is a free translation from me
"The sum of two numbers is 3.4 .If we take each of them and summed with they square, the product of it would be 18.5856. The lowest of those number is in the interval...
The problem
I am trying to write the equation for the plane on the following form ## ax + by + cz + d = 0 ##
$$
\begin{cases}
x = 1 + s - t \\
y = 2 - s \\
z = -1 + 2s
\end{cases}
$$
The attempt
## s, t ## are the parameters for the two directional vectors which "support" the plane.
$$...
I'm trying to find a closed form (an algebraic solution) for the following system:
x² - y² = 5
x + y = xy
It's a bit tricky but I manage to end up with the quartic equation:
x^4 - 2x^3 + 5x^2 -10x + 5 =0
And this is where I get stuck looking for a closed form root.
Any suggestion would be...
$a,b,c \in N$, and the following equation system is given :
$\left\{\begin{matrix}
ab+bc+ca+2(a+b+c)=8045-----(1) & & & & \\
abc-a-b-c=-2-----(2) & & & &
\end{matrix}\right.$
find the value of $a+b+c$
It's part of finite elements analysis.
All I need is to solve F=Ku,K is [12x12] matrix .
Some of the members of u are zeros ,some members of F are known forces . K is all known .
How do I solve F=Ku in that way ??
Thanks in advance.
find the solution of the equation system:
$\begin{cases}
a=\dfrac{b+c+d}{3}---(1)\\
b=\dfrac{a+c+d}{5}---(2)\\
c=\dfrac{a+b+d}{7}---(3)\\
d=c+5600\,\, ---(4)\end{cases}$
here $a,b,c,d>0$
Homework Statement
v_{f1}^2 = v_{01}^2 - m_{1}/m_{2} * v_{f2}^2\\ v_{f2} = m_{1}/m_{2} * (v_{01} - v_{f1})
Solve for Vf1 algebraically. How to solve this in the easiest way without having miles of calculations?
Homework Equations
The Attempt at a Solution
When I try to use the...
Homework Statement
Example:
x'=y-x^3
y'=-x-y^3
Homework Equations
The Attempt at a Solution
Linear system
x'=y
y'=-x
Is stable because Det(P-\lambdaE)=\lambda2+1
\lambda1,2=+-i
So if I am not mistaken,than Ishould use Lyapunov stability,because the linear system is stable and I can't say...
Dear All,
Recently, I have measured a series of nonlinear vibrational spectra from which I would like to extract some useful information about kinetics of the exchange process occurring in the studied system.
I need to fit my experimental data to kinetic model that is a solution of coupled...
I have a quick question.
I have to write the differential equations in matrix form
Eq1:= x1'(t) = -a1*x1(t) + vf
Eq2:= x2'(t) = a1*x1(t) - a2*x2(t)
is this correct :
Homework Statement
Solve this equation system for x, y and lambda.
\left\{\begin{matrix}
2x = \lambda (2x-6y)\\
2y = \lambda(-6x-14y)\\
x^2-6xy-7y^2+80=0
\end{matrix}\right.
The Attempt at a Solution
I really tried A LOT of things, but I can't solve it. I think it is not helpful to post...
Homework Statement
Consider the following linear system of equations:
x1+2x3-5x4 = 0
x1 + 4x2 +4x3 – 5x4 = 10
x1 + 2x2 + 3x3 – 5x4 = 5
4x1 + 2x2 + 9x3 – 20x4 = 5
b) Solve the equation system with the Gaussian method.
c) The solution set describes a plane. Specify it in the parameter...
Hello, everyone.
I'm working on simulating shallow water flow. I'm using the MacCormack scheme and fractional predictor-corrector steps. The Dxy factor should make the equation system stable but no matter what numbers I input, the results skyrocket, up to 10^80 and more.
Has anyone worked...
Hi i found a question in number theory, involving two equations, it goes as follows:
Let p1, p2, p3 and p4 be 4 different prime numbers satisfying the equations
2p1 + 3p2 + 5p3 + 7p4 = 162
11p1 + 7p2 + 5p3 + 4p4 = 162
Find all possible values of p1p2p3p4.
Not knowing what to do, i used the...
Hello, friends. I just registered because I desperately need some help.
Homework Statement
For my bachelor's degree in physics, I'm trying to simulate gravitational microlensing of a background source on a system of objects, acting as gravitational lenses. I have the equation up and running...
Homework Statement
For t\in\mathbb{R}, let:
A=\left[\begin{array}{ccc}
-1 & 0 & 0\\
0 & 2 & 2t\\
0 & 0 & 2\end{array}\right]
Get the solution for the general equation: X'=A(t)X
Homework Equations
The Attempt at a Solution
I done many of these problems, all with constant...
Homework Statement
Find the general solution of the system of differential equations
x'=10x - 12y
y'=25x - 30y
(where primes indicate derivatives with respect to t) by using the initial conditions
x(0)=A
y(0)=B
Homework Equations
The Attempt at a Solution
x''=10x' - 12y'...
given the matrix A and vectors X & B
A=
1 2 3
2 k 6
0 0 k-4
k 2k 3k
X=
x1
x2
x3
B=
2
4
0
2k
what values of K(if any) will give AX=B--
a) with no possible x1 x2 x3
b) with a single x1 x2 x3, what are they
c) with infinite options, including 1 free parameter? what is this...
[b]
Homework Equations
The equation is, given to me by lurflurf,:
mv' + f(v ) + s(u) = F(t), t > 0, u(0) = U0, v (0) = V0
where v=u'
For the record the equation was:
mu'' + f(u' ) + s(u) = F(t), t > 0, u(0) = U0, u' (0) = V0 .
The Attempt at a Solution
def rhs(u, t)...
hi guys,
I'm solving a pretty complex problem: calculating a trajectory of a charged particle in a custom magnetic field. I arrive to the point where this very nice equation system blocks my way :P
http://ramses728.altervista.org/img/phys.jpg
hope you can help me somehow