1
vote
1answer
40 views

Transforming a nonlinear system to a linear system

Suppose I have two points in $\mathbb{R}^2$ and I wish to find values of parameters $a$ and $b$ such that I obtain the power law $y=ax^b$ which goes through the two given points. I can solve the ...
1
vote
1answer
28 views

Using jacobian to solve a nonlinear system of equations?

I have to solve a system of nonlinear equations using jacobian but I'm not sure how to solve for the solutions. I remember one of my friends doing $Ax = B$; where jacobian matrix was $A$, but im not ...
2
votes
4answers
92 views

Solution to a system of nonlinear equations

Do you know any method to solve the following system of nonlinear equations ? $\begin{equation} 141,3829=A+\frac{B}{323}+5,78C+F323^{E}\\ 69,07645=A+\frac{B}{333}+5,81C+F333^{E}\\ ...
12
votes
2answers
650 views

System of non-linear equations.

I have to find all triplets $(x,y,z)$ that satisfy: $$x^{2012} + y^{2012} + z^{2012} = 3\\x^{2013} + y^{2013} + z^{2013} = 3\\x^{2014} + y^{2014} + z^{2014} = 3$$ I've found the trivial solution ...
2
votes
2answers
43 views

where did I go wrong in solving this sytem of nonlinear first-order ODEs?

To communicate my experience level and intent: I'm an undergraduate, this is not homework, I'm trying to write a physical simulation for fun and xp and am stuck just before (what looks to me like) the ...
0
votes
0answers
31 views

Reflection Symmetry for Non-Linear Differential Equations

We are given the equations: \begin{align} \dot{x}& =\mu \, x +y+y^3 \\ \dot{y}& =2x-2y+xy^2+\gamma \, x^2y \end{align} The question at hand is to determine whether there is some sort of ...
0
votes
1answer
42 views

Are there standard approaches, to solving a system of nonlinear PDE?

If we have a system of PDE's, where each PDE is different i.e. for $u:U\subset \Bbb R^2\to\Bbb R^3$, $u(x,y)=(a(x,y),b(x,y),c(x,y))$, which needs to satisfy $ \left\{ \begin{array}{ll} ...
4
votes
2answers
61 views

Solve numerical system of nonlinear equations?

I need to solve a nonlinear system of equations that looks like this ...
4
votes
4answers
108 views

Solve system of nonlinear equations using non-numerical method

Is there any non-numerical method to solve this kind of system of nonlinear equations for $c_1, c_2, x_1, x_2$: $$c_1+c_2 = 1$$ $$c_1x_1+c_2x_2 = 1$$ $$c_1x_1^2+c_2x_2^2 = 2$$ $$c_1x_1^3+c_2x_2^3 = ...
1
vote
1answer
82 views

solving a non-linear (trigonometric) system of equations with two equations and two variables

I'm trying to solve the following system of equations: $$l_1*sin(\alpha)=l_2*cos(\gamma)+l_3*sin(\beta)$$ $$l_2*sin(\gamma)+l_1*cos(\alpha)=l_3*cos(\beta)+l_4$$ with the unknowns $\beta$, $\gamma$ ...
1
vote
1answer
40 views

How to solve system of nonlinear differeintial equations

System follows: $$ y'=\frac{y^2}{z-x}; z'=y+1$$ I was found the 2 ways. The both are wrong 1) $$z = x + \frac{y^2}{y'}; z'=1+\frac{2yy'^2-y^2y''}{y'^2}=y+1; => (p(y) = y')=> yp(yp'+p)=0;$$ ...
0
votes
0answers
42 views

Solving equation for powers

I would like to find $\gamma$ in: $$ \sum_{i=0}^n x_i^\gamma = y $$ where $n$, $0 \leq x_i \leq 1$ and $0 \leq y \leq n$ are known. Also, $n$ can be fairly large (i.e. from a few thousands to a few ...
1
vote
1answer
40 views

Can the variables of $y = A + B \mathrm{e}^{C t}$ be solved analytically given 3 sets of points?

Given the non-linear equation $y = A + B \mathrm{e}^{C t}$ and 3 sets of points: ($y_1$, $t_1$), ($y_2$, $t_2$), ($y_3$, $t_3$), can the variables $A$, $B$, and $C$ be calculated analytically? ...
5
votes
2answers
124 views

Why does the following nonlinear system have 21 solutions?

I am curious as to why the following nonlinear system has 21 solutions (according to Wolfram Alpha). $$y+xy^2-x^3+2xz^4=0 \\ -x-y^3-3x^2y+3yz^4=0 \\ -\frac{5}{2}y^2z^3-2x^2z^3-\frac{z^7}{2}=0$$ I ...
0
votes
0answers
104 views

solving a system of algebraic equations

I'm trying to solve the following system of nonlinear algebraic equations for $q_{e}\in\mathbb{R}^{4}$ $$ ...
0
votes
0answers
25 views

limitations of non linear multivariant equation solvers

I have a system of non-linear multivariate equations. I am only interested in the roots of the system in an interval of each variable. For example, $$ \begin{align} \frac{1}{10} \sin \left( \frac{x ...
0
votes
1answer
75 views

When does this non linear 2 equation system have solutions? What is the solution?

I need to solve the following system: $$ \begin{cases} a x_0^2 = \exp{ \left( -\dfrac{x_0^2}{4 \sigma^2} \right) } +a r^2 \\ \exp{ \left( -\dfrac{x_0^2}{4 \sigma^2} \right) } + 4 a \sigma^2 = 0 ...
1
vote
0answers
56 views

how to solve these kind of systems $x^2+y^2=z^2; z-y^3=5; xy=z$

Three variable system of equations with three variable with exponents for example $x^2+y^2=z^2$ $z-y^3=5$ $xz=y$
3
votes
1answer
45 views

Solution to a trigonometric system

Find the solutions of the system $$\sin a-\frac{\sqrt{3}}{3}\sin b=0$$ $$\frac{\tan 2a-2\tan a}{\tan 2b}\cdot\frac{\tan 2b-2\tan b}{\tan 2a} =1$$ How to work with them ? Thanks
1
vote
2answers
133 views

Determine the number of solutions of nonlinear system without solving.

$x^2-y^2+2y=0$, $2x+y^2-6=0$ I need to determine the number of solutions without solving it. There is a hint that a graph can help but I am still not sure how to go about this. Thanks
1
vote
2answers
82 views

Solution of a non-linear system

What is the solution of the following system? $$ \begin{align} a \cdot e-b \cdot d & =\alpha \\ a \cdot f-c \cdot d & =\beta \\ b \cdot f-c \cdot e & =\gamma \end{align} $$ Where the ...
3
votes
1answer
72 views

a system of equation

I want to show that the following system of equations does not have a solution, but I do not know how to do this $$w_1+w_2=\frac{1}{2}$$ $$w_1s_1+w_2s_2=\frac{1}{6}$$ $$w_1t_1+w_2t_2=\frac{1}{6}$$ ...
1
vote
2answers
180 views

How to prove the existence of solution of a non linear system of equations

Writing the ortogonality condition for any element of O(n), I've arrived to: If we take n=2, we know that $\Lambda\Lambda^{T}=\mathbb{I}$, so: $$\begin{pmatrix} x & y \\ z & t \end{pmatrix} ...