Non-linear Definition and 340 Threads

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...

I have a set of non-linear ODE. There are eight variables that depends on time (t) 4 of those are first order ODE 1 of those are first order non-linear ODE 3 of those are non-linear equations The variables are (t) (p) (ps) (gs) (gd) (as) (ad) (hs) (cs) k1,k2,k3,k4,k5 are...

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...

What makes a PDE non-linear please? Thanks!

i,m stuck into solving this differential equation: \frac{dy}{dx}f(y)=1 i,m trying to find an integrand factor but don,t know what to chose to solve it someone could help?..thanks... EDIT:i,m interested in getting y=y(x) not x=x(y)

in the movie "the bank" a mathematical genius predicts the exact movements of the sharemarket after years of research and attempts. he uses Fractal geometry, chaos theory, non-linear dynamics and of special interest to him was the work of mandelbrot and his work regarding fractals. He...

How non linear fea works. I am studying that and i can't find any material in the web which has some basics. How the Newton raphson method is used in non linear fea suppose i apply a force f on a structure after that how non linear fea works?

Who has any litterature about non-linear differential forms, especially for example if I would like to compute the following : (dx\wedge dy)(dx\wedge dy\wedge dz) is it equal to (dx)^2\wedge (dy)^2\wedge dz ?? Thanks in advance.

This was sent to me as a personal message- it's always better to post questions like this than just send them to me!

Non-Linear Functions Introduction: When a golfer hits a golf ball squarely at the bottom of the swing, with the shaft perpendicular to the ground, the ball is propelled into the air in a direction perpendicular to the face of the club [see the diagram below]. The different club angles...

Non-Linear Functions Introduction: When a golfer hits a golf ball squarely at the bottom of the swing, with the shaft perpendicular to the ground, the ball is propelled into the air in a direction perpendicular to the face of the club [see the diagram below]. The different club angles...

Now this next post is actualy connected to my previous post about light speed. Now what the light speed is infinite also shows is that there is no external time what so ever. What i mean is the big bang is happening right now just as the possible end of the universe is happening right now...

take a point A(x_1,y_1) on a circe centre B (x_2, y_2) and allow the circle to roll along an X-axis; now we all know that the cycloid equation to point A is highly non-linear; so now if we take the point B, we find the problem has been converted into a linear problem; now do this to E-fields...

Hi Everybody, Does anybody know how to solve, analytically or numerically, the following differential equation : \frac{d^2\Phi}{dx^2}-a.Sinh(\frac{\Phi}{U_{th}})=-b.Exp(-(\frac{x-x_{m}}{\sigma})^2}) The unknown function is \Phi. a and b are some strictly positive constants. q\Phi is...

The energy of a spring is the work done on the spring, and for a simple spring with F=-kx the energy may be changed by changing the constant k. In the non-linear case eg F = kx - 4qx^3 we would take the integral to obtain energy. But the question I thought was trivial was, "what values of k...

Im using maple, how can i find the general solution of y''y'''=y and then find the terms up to degree in taylor series using this general solution? Thanks

Does anyone know anything concrete about the application of nonlinear chaotic dyamical systems to psychology? I have come to find out that there is a substantial amount of research being done on this. I read some articles today where people were trying to apply this to dysfunctional families...

Given a system of two equations and two variables, x and y: x + ay = c x + by2 = d I believe this system can be solved uniquely (please correct me if I'm wrong). My question is that of independance. Would one be correct in the statement that these two equations are linearly independent...

I know that there is a general analytic method to solve the following non-linear differential equation \frac {dy} {dx} = ay^2 + by + c … where a, b and c are constants. It is just a Riccati equation generalized to constant coefficients. I am wondering if there is a analytic method to...

Very often I'll clap my hands while my cats' back is turned because I hate him. Most of the time he jumps just before my hands actually clap. I sometimes try to "fake" a clap by not actually making contact, but of course this doesn't make him jump, because in the future there was no clap. I...

I don't have a problem with drawing up matrices for system solutions, but I'm often puzzled by the answers. I therefore have avoided matrix analysis, even though it obviously, in a given case, would make a very nice short-cut. (Especially with computers: Other modalities can be technically...