Non-linear Definition and 318 Threads

Hi, Does anyone knows how to solve this 2nd order non linear differential equation with exponential components? d"V/dx" = A*exp(-B*V)-C*exp(B*V) where A, B, C are constants. Thanks

Hope I have posted this in the right section, this question is half differential equation and half finite difference method. The equation I have is a form of the Lucas Washburn equation, which is concerned with capillary rise...

Hello, I'm a student from Lithuania. I have found in one forum topic your discussion about non-linear equation convertion into a linear form.. I have some problem with that...Could you help me, please? :) For, example, I have two non-linear models: 1. y = a [1/(1+b/(c+x))]*exp(-d*x) 2. y =...

I'm interested in coming up with an function that approximates the solution to a non-linear differential equation. (There is no known closed form solution) The equation is Y''=(1/Y)(Y')^2-Y*A+Y^2*A where "A" is a constant, and Y' and Y'' are the first and second derivatives with respect to...

could anyone help me with solving this second order differential equation? I am a noob on here so not sure how you get the mathplayer stuff on... so the equation is of the form x'' +ax' + bx^n = 0 (x^n means x to the power n, with a and b constants). i tried substituting x'=u to get a first...

hi, Do the addition of non-linear terms in action play any significant role in string theory?? if so, what is its significance in string cosmology? --- anuradha

Hey Guys, I am really confused about the first problem on my first problem set in Diff Eq (not auspicious is it? Oh well...) Draw the Direction field y' = y -y^2. Identify Isoclines and any equlibrium solutions. I don't understand how to approach this problem because doesn't the y^2...

Hi, I have a non-linear function F: \Re^{3}\rightarrow\Re. I would like to find the roots of this equation numerically, since an explicit formula cannot be derived. As far as I am aware Newton's method can only be utilized when the domain and the range of the function are of the same...

Dear All, I have maybe quite a naive question: Does there exist a result that a generic system of non-linear equations have a unique solution? (defined from R^n to R) Similarily as it exists a result that a generic square matrix could be inverted? Waiting impatiently for news...

Homework Statement I am modeling a set of equations for a protein network. It is a feedback loop between 2 proteins. I have gotten the differential equations for this model and plan on doing an extended Kalman Filter to estimate the levels of protein in real time. However, I am having...

Dear all, I have a set of 5 non-linear equations with highly complicated and long forms for which I wish to find the unique solution. I was going to tackle this problem with Broyden's method since the derivatives cannot be easily found. However, even if I get a solution from this, this is...

I don't know very much about DEQs, can someone point me in the right direction for solving this? Note: \phi is a function of another variable and C_1, C_2 are constants. -\phi ^2 \cdot C_1=\frac{1}{1+\phi ' ^2}+C_2 I have tried trig sub, but I didn't get anywhere. Regards...

Question on Newton’s Method of solving systems of non-linear equations. I understand the concept for a single non-linear y=f(x) solved for zero, but am confused about systems of non-linears. If I take two functions U(x,y) and V(x,y), am I solving for the points where they intersect with each...

infinite series solution for NON-linear ODEs? Is it possible to use the infinite series method (Frobenius) to obtain general solutions of non-linear ODE's, I want to try a second order equation. Any good references where I can see how that goes exactly?

Hello, I have the 2nd-order nonlinear ODE below: k(v)=\frac{\phi ''(v)}{\phi (v) (\phi ' ^2 (v) +1)^2} Where k(v) is some function. I would like to investigate for what functions k there can exist solutions on a given interval [a,b]. For example, if k(v)=0, then \phi '' (v)=0 which implies...

Hey folks, Does anyone have any experience with how to solve non-linear ODE's numerically, perhaps in mathematica?? I am trying to solve the following equations: 3H_a^2+3H_aH_b=K_1 \dot{H}_a+3H_a^2+H_aH_b=K_2 \dot{H}_b+3H_a^2+3H_aH_b=K_3 Where H_a and H_b are both...

Hey everyone, Having some trouble here using the solver we were supplied and modifying it to fit our problem... I have a wire with a current flowing through it. I'm trying to find the temperature distribution wrt. position in the wire. BV's are: T(x=L/2) = 300K dT/dx (x=0) = 0 (Apparently...

Hi all, At the moment I am trying to find a best fit equation to radial velocity data vs. time of a planet HD17156b. The paper with the Authors fit parameters (I am trying to mimic the fit) has the arXiv ref number of :0704.1191v2 From this paper I extract their data, which is on the final few...

I'm having trouble solving this differential equation: (2x^2)yy' = −1 I'm just really not sure how to go about solving this.

Hello everyone. My question is quite long, so please bear with me; my professor is very busy and cannot help me at the moment, and I can't contact the course tutor. We have the DE \ddot \theta + \alpha \dot \theta + \sin{\theta } = \epsilon \cos{\omega t} where theta is the angle the...

Now we've all been taught how to use the average. Let me give 2 examples to those who don't know. Example 1: Say an object moves with velocity 3t in the time t=0 till t=2. Find distance covered. Initial velocity = 0. Final velocity = 6 disp. unit/ time unit. Avg. Velocity = 3 disp...

http://img132.imageshack.us/img132/5153/njga7.jpg Question 8 is the question I need, but 7 has relevance for it. I have my equilibrium points, and am stuck on two of them with the same problem. 1 of my points (H,P) = (0,L) - No hunters, but prey. I put this into my jacobian matrix, and I...

Dear everybody, I wave an equation with datas and want to regress in non linear form with plot. Would you help me to solve the equation bellow by any softwares, please? The data, the equation and parameters are given bellow. I want to fit the data to non-linear equation to find Df and k...

Find the inverse of the (nonlinear) transformation from R^2 to R^2 given by u=3y v=3x^7-6y x=? y=? The Attempt at a Solution - I'm really not sure what to do on this problem. We haven't seen any problems even similar to it in class, so I'm looking for help on it.

I have 15 equations with 15 unknowns describing a dynamic process. I would like to know how I can conbine solving non-linear equations together with ordinary differential equations (1st and 2nd order) simultaneously, without using ode45, but Euler's method.

Hello, I am currently trying to design a system that will sychronize two propellor motors, and I must design using the following equation: w'*I + (w^2*r^2*p*S*C_d)/(2) = T_t + T_ss w' = Angular acceleration I = moment of inertia w = angular velocity r = radius of blade p = air density...

Homework Statement Obtain the fixed points for the following as a function of a, where 0<a<infinity: f(x)=tanh(ax) Homework Equations The fixed point is given by f(x^{*})=x^{*} The Attempt at a Solution It's basically a math problem: tanh(ax)=x Find x in terms of a. I tried it two...

Given that F(x,y)=xy(x+y-1). Determine whether S={(x,y) | F(x,y)=0} is a smooth curve. Now, F(x,y)=x2y + xy2 - xy Let gradient F = (2xy + y2 - y, x2 + 2xy - x) = 0 So 2xy + y2 - y = 0 and x2 + 2xy - x = 0 In order to determine where S is smooth, I have to solve these 2 equations for x and...

I want to first explain my current understanding and motivation so you guys can whip me into shape in case I'm misunderstanding the starting point -- SR and linear transformations. So, we can write the laws of electrodynamics in terms of the electromagnetic field tensor F^{\alpha \beta} as...

Homework Statement Given y1=x^2 and y2=1 are two solutions of the DE y"=(x/y)y' Are the functions -y1 and y1 and y2 also the solutions of the equation?If not why? Homework Equations The Attempt at a Solution I cannot see how to proceed.However,I can see that it is a non-linear DE...

Non-linear ODE, "blow-up" phenomenon On page 40 of Steven H. Strogatz's Nonlinear Dynamics and Chaos, question 2.5.2 says: Show that the solution to x' = 1 + x10 escapes to positive infinity in a finite time, starting from any initial condition. (Hint: Don't try to find an exact solution...

NOn-linear equation, when has a solution?? For linear system of equations: A_{ij}x^{i}=b_{j} (implicit sum over repeated indices) a necessary and sufficient condition to exist is that |detA| >0 but what happens whenever you have a Non-linear equation: f(x_{i},x_{j} ...

hey does anybody have any idea how to solve this equation? E/m= xd^2x/dt^2with initial conditions x=a and dx/dt(a)=0 its non-linear and so I don't have any idea what to do with it, and maple won't give me an answer.

On a physics test today, one of the free response questions asked about a non linear spring where F=-kx^3. Now I got everything right, but there was one thing that I felt I did not have any concrete mathematical basis for--I just thought about it. I had to say whether increasing the amplitude...

Hi All; Long time reader, first time poster. Here's a tricky one. I have a solid state NMR set of data in 3D. Let's say the signal phases in the three dimensions are: exp(i*(A+B*C+C)t_1) exp(i*(A+B*C+C)t_2) exp(i*(A+B*C+C)t_3) given the information, one should be able to (in theory)...

I was wondering how you could paramatize a non-linear curve between two points (1,0) and (a,b) I have been trying to do like a parabolic paramatization but I am getting nowhere I can get the first point alright x=x y=1-x^2 1<x<a but then you get y=1-x^2 Any suggestions

Let's suppose we have a Non-linear operator (supposing is self-adjoint and all that) so: cos(y'')+(y')^{2}y+xy=g(x) with the boundary conditions for some a and be real y(a)=0 and y(a)+2y(b)=0 then the "superposition principle" can't be applied so how the hell do you solve it :mad: :mad...

Hello learned colleagues and other deep thinkers: This question may be construed as either way too esoteric, or simply as too vague for this forum, and if deemed either of these I would agree if others find it an inappropriate topic. However... When it comes to aerospace vehicles and the...

Hi guys, just wondering if you can give a hand on a non-linear ODE, all you guys need to do if give me a good substituion to try... xy''+y'+(y')^3 = 0 where ' = d/dx

Hi, can someone please help me with the following differential equation? I need to find the general solution. x\frac{{dy}}{{dx}} = x^2 - y^2 It's non-linear so I didn't bother with rearranging the equation. It doesn't look seperable either so that doesn't really leave me with much to...

Let be the NOn-linear Schroedinguer equation: i\hbar \frac{\partial \psi}{\partial t}=-\hbar^{2}(2m)^{-1} \nabla ^{2} \psi + |\psi|^{3} for example..the question is..how the hell do you solve it for certain boundary conditions that the Wavefunction must satisfy if you can,t apply...

How would one go about finding an analytical solution to the following ODE note that we are trying to find y(x) subject to... (x*y'')^2 - (1 + (y')^2) = 0

Lets us a potato gun for an example. Having a source tank filled with air, and when a trigger is activated, the air is dumped straight threw the valve and out the tube. --> --> --> --> What would happen if the flow of air had to go out of the pressurized source (~160 psi ~40 cu. in...

Hi, I've collected some data on the relative permeability of ferrite at various temperatures, subject to a constant external magnetic field and I'd like to fit a curve to the data. I believe that stat-mech theory predicts that \mu_r = 1 + a\tanh(b/T) where T is thermodynamic temperature...

Hello All, I was hoping one of the many knowledgeable people on this forum could give me some helpfull advice on how to proceed with the following problem. Basically, I am trying to fit experimental data to a curve. In general my curve looks like this and I know the constants have the...

Hi! I'm a French student and I have some work to do about non-linear optics, and I'd like to see an American approach to this discipline, which is said to be slightly different from ours. So, does anyone know any relevant website about this topic? Or anything that could give me information...

In another thread, PF member "SelfAdjoint" made the following comment: ...and indeed you see papers suggesting non-linear replacements for QM and nonlocal replacements for relativity... I am interesting in reading such papers that "suggest" non-linear replacements for quantum mechanics (QM)...

I did some number crunching and found the following: Given n equations in n unknowns: a*f(x) + b*g(y) = c d*f(x) + e*g(y) = f If there is a solution to these equations, you can use substitution to transform these equations into a set of linear equations and solve using linear algebra...

For my first year formal lab I am having a little bit of trouble with one aspect, let's see if anyone can help Im trying to rearrange the equation T = 2pi [(32 L I)/(pi S d^4)]^1/2 ...(sorry, i don't know how to use the better way of displaying math) to form a linear equation so it can...

It seems to me that Linear Regression and Linear Least Squares are often used interchangeably, but I believe there to be subtle differences between the two. From what I can tell (for simplicity let's assume the uncertainity is in y only), Linear Regression refers to the general case of fitting...