# Tagged Questions

In mathematics, a nonlinear system of equations is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree ...

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### Analytical solution for a Non-linear differential equation $\frac{d^2y}{dt^2} = A\left(\frac{dy}{dt}\right)+B \sin(2Cy)$

Analytical solution for a non-linear differential equation: $\frac{d^2y}{dt^2} = A \left(\frac{dy}{dt}\right)+ B \sin(2Cy)$ A,B are non-zero constants and y (position) is a scalar-value parameter ...
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### Underdetermined, nonlinear system solvability criteria

The system under consideration is of the following form: $\ A(x)*x = \ B(x)$ In my case, this is a highly nonlinear underdetermined problem. Was wondering whether there is a way to determine ...
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### Control of Nonlinear Cascaded systems

For control of cascaded linearized system, my objective is to design a stabilizing controller. For stability and performance analysis of such structures, I have been trying to find a book where such ...
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### What it this theorem saying? - Regions of state space for which the flow eventually exists…

We have been given the following theorem to define regions in the state space for which the flow eventually exists. In questions, we use it to show that all trajectories eventually enter a bounded ...
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### How should I approach solving non-linear equations?

I need help creating a method for a program I'm making. I've worked on this countless hours and I can not seem to figure it out. what I need: A method that returns $x$. My variables ( initialized to a ...
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I have two equations, $$\frac{x}{1-x}=\exp(A_{x}+Bx+Cy)$$ $$\frac{y}{1-y}=\exp(A_{y}+Cx+Dy)$$ I am interested in the number of solutions $(x,y)$ to these two equations as the parameters $A_{x},A_{y},... 1answer 34 views ### What does a negative time stepping mean? (Adaptive time stepping) Summary behind the problem: The following code aims at solving a static elasto-plastic problem. Like a 2D square mesh based on an elasto-plastic constitutive model like Von-Mises or Drucker-Prager ... 0answers 11 views ### Nonlinear ODE Grimshaw solution manual Anyone has a solution manual for Grimshaw's 'Nonlinear ODEs.' I had this class and really enjoyed it. Wanted to solve the rest of the problems in the book. If anyone possess a solution manual let me ... 0answers 17 views ### Complex Least Squares With Magnitude Equality Constraints For$\mathbf{x} \in \mathbb{C}^N$, I'd like to solve the following problem: $$\mathbf{x}^\ast = \arg \min_{\mathbf{x}} \Vert \mathbf{Ax-b} \Vert_2 \,\,\,\,\,\, \mathrm{s.t.} \,\,\,\,\, \Vert x_i \... 0answers 6 views ### Closed-form solution for a simple system of concave equations I am trying to solve what looks like a simple system of equations:$$x_j = A_j\left(\sum_{i=1}^n B_{ij} x_i\right)^\alpha $$for all j\in\{1,\dots,n\}, where n is a positive integer, 0<\... 1answer 30 views ### Analytical solution of a non-linear equation with a 'min' function I am building a mathematical model of a non-linear dynamical system and I have an expression of this form:$$x=\min\left(\frac{y}{a+y},\frac{y}{c+y(d+ex)}\right)$$or let's consider any form like:$...
Say I have a sinusoidal function $s(x)=\alpha \sin(\beta x - \gamma) + \delta$ and the linear function $f(x)=mx+b$. How can I find $x$ exactly such that $s(x)=f(x)$? I can't solve it like a normal ...
$g(x)=x \log(x+1)+x-1$ where the log has the base $e$. Set $G_1(x)=1/(\log(x+1)+1)$ and $G_2(x)=1-x\log(x+1)$. Show that the zero $x^*$ of $g(x)$ is a fixpoint of $G_1(x)$ as well as $G_2(x)$. My ...