Non-linear Definition and 318 Threads

Homework Statement Find a solution (Z2) of: z'' + 2z - 6(tanh(t))2z = 0 that is linearly independent of Z1 = sech2Homework Equations The Attempt at a Solution reduction of order gives you v''(t)(Z1(t))+v'(t)(2 * Z1'(t)) + v(t)(Z1''(t)+p(t)Z1'(t)) = 0 however the third term on the LHS can be...

Homework Statement Show that w(t) = tanh(t) solves the nonlinear problem: w''(t)+2w(t)-2w3(t) = 0 t ε ℝ Homework Equations \frac{d^2tanh(t)}{dt^2} = -2tanh(t)sech2(t) = \frac{-8sinh(2t)cosh^2(t)}{(cosh(2t)+1)^3} tanh(t) = \frac{sinh(2t)}{cosh(2t)+1} tanh(t)3 =...

Homework Statement I am having problems solving this system of non-linear equations in Matlab and Mathematica. a,b,c,d,e,f are all independent variables. In Matlab I use fsolve() and get one solution, in Mathematica I use NSolve[] and get another totally different solution. Mathematica...

Hello, I'm studying for a test and this is a question on a practice test... cos(x)+y^2+(2yx-1)y'=0 I can't separate the variables (it's not homogeneous, either), this isn't exact and bernoulli won't work... dy/dx=-cos(x)/(2yx-1)-y^2/(2yx-1) I changed the equation so it would look...

Matlab -- How to solve simultaneous non-linear differential equations? How to solve simultaneous non-linear differential equations in MATLAB m-file without using the commands?. can you give me the program?.

1. i am stuck 2. The profit function is given by P=-2x^2 + 60x - 250, where x units is the quantity and P the total profit. Find the maximum profit and the number of units where maximum profit occurs. Sketch the curve of the profit function. 3. i can't do anything, my brain just jammed...

Homework Statement The curve y = ax2 + bx + c passes through the points Q(x1,y1) R(x2,y2), S(x3,y3). Show that the coefficients a, b, and c are a solution of the system of linear equations whose augmented matrix is x12 + x1 + 1 = y1 x22 + x2 + 1 = y2 x32 + x3 + 1 = y3 Homework Equations The...

Homework Statement I need to solve this differential equation numerically. I hope you can help me, it's not homework! Homework Equations This is the equation to be solved x''=\dfrac{\alpha}{x}-\beta\dfrac{(x'-\gamma x)^2}{x}-\delta x - \dfrac{\varepsilon}{x^2} The Attempt at a...

I have non-linear system of ordinary differential equations to solve by first linearising it. I know it can be linearised by expanding right side of equations by Taylor series and keeping only the linear terms. Then I can solve the linear system of differential equations with given initial...

I need to design a cam based on the following math problem: A non-linear force f(n) is working on a lever that is x + x' long (x+x'=constant). I need an equation for the ratio, x/x', such that the counter-balancing force, f', is constant (non-varying). By varying the ratio of f(n) to f', that...

Hello. I am trying to solve this problem methodically but my solution does not seem to agree with the given answer. Homework Statement The differential equation is: (sinx)y' - (cosx)y = 1 + C Homework Equations The Attempt at a Solution y' - (cosx/sinx)y = 1/sinx + C/sinx When finding the...

system is $x'=y+xf(r^2)$ and $y'=-x+yf(r^2)$. where $r^2=x^2+y^2$ (i) prove that $\frac{dr^2}/{dt}=2r^2f(r^2)$. My solution ( I won't write out details): use chain rule and the fact that rr'=xx'+yy'. (ii)assume $f(r^2)$ has N zeroes. determine the number of fixed points and periodic solutions...

Homework Statement I have: \dot{x}=4x+y-x(x^2+y^2) \dot{y}=4y-x-y(x^2+y^2) And I need to find \dot{r} and \dot{\theta} 2. The attempt at a solution I got as far as: \dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4)) \dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta)) How do I...

Homework Statement I just need to know how to start this. I've never seen a piece wise ODE before and I don't really know where to start to be honest. I know it's non-linear and it's of order one. dy/dx = (1/3)y - 3, y > 0 and dy/dx = -(1/3)y - 3 ≤ 0. y(0) = 1 with y(x) \in C0...

Hi. In the course of trying to solve the field equations of a physical system, within some assumptions about its symetry, i managed to get a non-linear ODE involving only a single function of one variable, but still rather tough to handle : In the equation, x=x(r) is the unknown function to...

Could someone please tell me the fundamental differences between linear and non-linear waves?

When I'm reading a tutorial about Harmonic Balance algorithm (this is a link to the tutorial website), I'm quite confused by the concept it mentions about the nodal analysis of non-linear components, especially for: The non-linear circuit is modeled by its current function i(t) = i(v_1...

Homework Statement In control engineering, I want to have a mathematical model of a physical system as a set of input, output and state variables related by higher order differential equations. 2. Relevant concepts As we all know that, in control engineering, we can solve linear-system...

I have derived a 3rd order non-linear ODE with its respective boundary conditions, and I was hoping to get a hint on how to find a closed form solution to it. The equation is given as: F''' + (1/C^2)*F*F' = 0 Where the primes denote a derivative, and C is just a constant. Any help is...

Given the following sets of data, find the curve of best fit x = -4, -6, 5, -6, -9, -2, 5 y = -4, -7, 3, -12, -2, 5, 7 a) y = a + bx b) y = a + bx + c cosx I can do part a by using the formula for least square methods for straight line. But what about part b? One way I can think of is...

Homework Statement yy''-y'^2 = y^2lny The Attempt at a Solution well, since the equation is of the form f(y,y',y'')=0 I turn it into the form f(y,p,p dp/dy)=0. After those substitutions are made, we'll have the following equation: yp (\frac{dp}{dy})-p^2-y^2 lny=0 which is a Bernoulli equation...

The original equation is: V'' - k*V^-1/2 = 0 I then said u = V' therefore u' = u(du/dV) so the new equation is : u(du/dV) = V^-1/2*k Im a little rusty on separation of variables but I got a u in the final answer which means I have to integrate again since I need the final answer...

Hi, I am trying to solve the following equation analytically. I think the solution shouldn't be that hard but I'm really rusty on these kind of things. V' - k*V^-1/2 = 0 where k is constant. Any help is appreciated, got to turn this in tomorrow!

Hi I have some data samples and and my job is to find a curve that will fit these values. The curve that i have gone for is in the form y = k * sqrt(d1^x*d2^y)*d3^z where kxyz are all unknowns that I need to find. I solve this with the MATLAB function fminsearch and the solution is...

How can a system of non-linear differential equations be solved using Mathematica? More specifically, I understand the process that needs to be executed, but I don't understand how to make it work syntactically. The process as I understand it: Four expressions are given in four...

I am running a non-linear analysis using ANSYS using multilinear isotropic hardening. The problem is that the value of maximum prinicipal stress I get on my model is greater than the max value in the table which I input. So I think ANSYS is extrapolating the values of stress on its own beyond...

hey forum, first of all, I'm a high school kid so forgive me if this is stupid. I've been thinking about relativity for some time now, and the issue with simultaneity. Einstein proposed that length contracts as you approach the speed of light. Assume for a second that a train is going...

Hi all, Hopefully this is the right section for my post, if not I apologize. I'm hoping I can just get some advice to help me get started in the right direction. I am trying to do a mathematical inversion for the following: \frac{1}{N(zi)} \frac{dN}{dz}|_{z=zi} = -\frac{2}{zi} -...

Let us consider the following partial differential equation: {(}\frac{\partial z}{\partial x}{)}^2{+}{(}\frac{\partial z}{\partial y}{)}^{2}{=}{1} ---------- (1) The general solution[you will find in the texts: http://eqworld.ipmnet.ru/en/solutions/fpde/fpde3201.pdf is given by...

Homework Statement A non-linear oscillator consisting of a mass on a spring has a potential energy of the form \frac{1}{2}kx^2 - \frac{1}{3}\alpha x^3, where k and \alpha are positive constants, and x is displacement. Using conservation of energy, show that the motion is oscillatory if the...

Homework Statement y''+(1/y)*(y')2=0 Homework Equations The Attempt at a Solution This is another problem I am having trouble with. I have done searches around the internet, but seen that all "non linear" ODE of second order involves a non linear form in a non differential term...

Hello, i am working on pulse propagation in optical fiber. i have to simulate the nonlinear Schrodinger equation using the FDTD (Finite Difference Time Domain) method. The Schrodinger equation has the form dA/dz = i/2 β2 d2A/dt2 –α/2 +iγ |A2|A where β2 is dispersion, α is...

Hi all, I have a question regarding least-squares, and I'm certain I can't be the first one to encounter it, but I've had no luck searching the literature for a solution. Here it is: Say we have a non-linear least-squares optimisation problem. We have data points y_i and a model y(x_i;{\bf...

can someone help me to solve this problem.i cannot remember how to solve the non-linear integration.like using chi-square distribution and uniform distribution. which one can i used to solve this integration?

I'm trying to solve the following ODE: ydx+(\frac {e^x}{y}-1)dy=0 I tried to transfer this ODE into exact form but no luck. Will appreciate any help.

Homework Statement Homework Equations The Attempt at a Solution I just want to ask how to obtain the solution? What mathematical method involved?

Hey, we have to solve the following problem for our ODE class. Homework Statement Find the solution of the initial value problem dx/dt = (x^2 + t*x - t^2)/t^2 with t≠0 , x(t_0) = x_0 Describe the (maximal) domain of definition of the solution. The Attempt at a Solution Well...

Hi I am trying to solve an analytical solution for a single-DOF system with a non-linear damping component: mx'' + B2x'x' + B1x' + Kx = 0. Tried in maple with no success with the non-linear term in the eqn. Thanks in advance.

Homework Statement I am trying to find the critical points of the system x1=x2+y2-2xy-1 and y1=y+x-2 Homework Equations x1=x2+y2-2xy-1=0 y1=y+x-2=0 The Attempt at a Solution I tried to solve for zero but I end up with multiple solutions way more then I should need any help answering...

Homework Statement Find the general solution to x3y'''-9x2y''+76xy'=0 Homework Equations I'm kind of confused on where to start. I'd suppose you'd throw in y=emx but I'm not positive since there are Xs in there. Once I know what to do with the x terms, I can just find all the roots and that'll...

For the solution to this problem, I have reduced the number of equations down from 17 to 6. Due to algebra reasons, these equations cannot really be solved symbolically (MAPLE tried, and return four full pages packed with symbols, just for one equation). These three equations need to be solved...

I know that Newtonian gravity as a theory is linear and GR is not, but I'm trying to get a feel for why textbooks often insist relativistic gravity must be non-linear, in order to account for the gravitational effect of "gravitational energy" itself (which is however not part of the source term...

Can someone please explain to me in layman's terms what a non-linear oscillator is? I need to determine if a ring pendulum is a non-linear oscillator, but I can't really do that without knowing what it is I am describing.

I'm having some trouble solving an equation that is similar to a Bernoulli equation. It is of the form \begin{equation} \ddot{x}+f(x)\dot{x}^2 = g(x) \end{equation} Where x is a function of time, perhaps. I feel moderately certain that there should exist an exact solution, but I've so...

u''+u'/x+C=0 u-function of x, C - const could someone solve it for me or at least give a hint??

Hi, I was wondering: What is the physical reason for only choosing linear operators to represent observables?

Hi I'm writing a function (matlab) in my numerical analysis class that descripes in a certain way a non-linear differential equations with Robin BC that I will then feed to a program that uses finite difference method to solve it. It seems to work but I wanted to look for a site or program that...

Homework Statement The cutting force developed during a particular machining operation is shown in figure (a). Model the system as a SDF with equivalent mass of the cutting head = 25 kg. The damping is linear viscous (ξ = 0.1), and the equivalent spring is nonlinear “hardening” spring of...

Homework Statement Solve y'=x^2+y^2 with initial condition y(0)=1. Homework Equations This is a first order ODE. The Attempt at a Solution I have tried separable variable, exact, and homogeneous and non-homogeneous, but none of them work. It's neither linear nor Bernoulli...

Homework Statement Is this invertible? If so, find the inverse. \left( \begin{array}{ccc} y_{1} \\ y_{2} \end{array} \right) = \left( \begin{array}{ccc} x_{1}^{3} \\ x_{2} \end{array} \right)Homework Equations The Attempt at a Solution I know that an invertible LINEAR transformation is a...