Nonlinear Definition and 558 Threads

Hello, How to solve the equation as follows: F''+F'*F'-k*F=0, where k is a constant and k>0 Is there any analytical solution?

Hi, what kind of technic should i use to solve the below DE? dx/dt=x^2-cx, where c is just a constant. Many thanks

Does anyone know how to solve the following Non-linear, second order, differential equation? A*y" + B*(y')^2 = F(t) + C where A, B, & C are constants **please note, in case the above notation isn't clear, the y' term is squared which is what makes it non-linear. Also, F(t) is time...

I was looking for some guidance on how to attack this problem. Consider the nonlinear ODE: y'(x)+y^{}2(x)+Ay(x)+B=0 (y prime + y squared with A and B constant coefficients) Show that the solution is given by y=z'/z, where z(x) solves the second order ODE: z''+Az'+Bz=0...

1. y' = a*(y^n) + c a, n and c are constants. Any idea about this problem ? How can it be solved ? i think there is no analytic solution thanks for your help in advance

Hi, I have a choice of taking this advanced ODE course, and I am wondering if this is worth studying. The course will cover mainly chapter 9 of Boyce/DiPrima textbook after we cover existence and uniqueness theorem. Chapter 9 is called "Nonlinear Differential Equations", and covers topics...

Hi. I have the following two equations S_{21}=\frac{(1-\Gamma^2)z}{1-z^2\Gamma^2} S_{11}=\frac{(1-z^2)\Gamma}{1-z^2\Gamma^2} How would you go about solving these equations? I want to avoid square roots because they make the results ambiguous. I myself have found that...

As far as I know, for an n-th order homogeneous linear differential equation, there are n number of linearly independent solutions and the general solution to the equation is a linear combination of them. In the case of nth order homogeneous non-linear differential equation can it be shown that...

Homework Statement I'd like to solve the following non-homogeneous second order differential equation and may I ask smart scholars out there to help me with this? y"(1-1.5(y')^2)=Cx^n, (^ denotes "to the power of") where C and n are constants, and the boundary conditions are: y=0...

Suppose there is a nonlinear differential equation in y(x) of the form: y''(x)(c_1+a^2y(x)^2)+p_1(x)y'(x)^3-by(x)y'(x)^2+p_2'(x)(c_1+a^2y(x)^2)+hy(x)=0 Where prime denotes derivative with respect to the argument x; p_i are known variables, and c,a,b,h are constants. Is there any way to write...

Hello everybody, I've come cross the following first order nonlinear equation when trying to solve for the speed of an electrical motor at any given time t during motor start. y'=-(ay^2)+bx+c ; y(0)=0 ; a, b and c are constants; y=motor speed; x= time The...

Hello: I discovered this forum while looking for advice on solving a first order nonlinear differential equation. The equation I am trying to solve is dy/dx=(3ay+3bx^2y^2)/(3x-bx^3y) a and b are constants. The equation is not exact, nor is it homogeneous. I have failed to separate the...

Hello: Can anyone help me solve with the following nonlinear 2nd order differential equation? d^2 y/dx^2 (1+a(dy/dx)^2)=bx^c (a,b & c are constants.) Thank you. younginmoon

hello I want to find exact solution of a nonlinear ode with its boundary conditions . the equation and its b.cs are written below : a*y''''+y''' y -y'' y' = 0 y(h/2)=V1 , y(-h/2)=V2 , y'(h/2)=0 , y'(-h/2)=0 where V1 , V2 , a and h are constant . although with...

I am solving the following simple looking nonlinear PDE: (\partial f / \partial t)^2 - (\partial f / \partial r)^2 = 1 Using different tricks and ansatzs I've obtained the following analytic solutions so far: f(r,t) = a\, t + b\, r + c, \,\,\,\, a^2 - b^2=1. f(r,t) =...

Ok, so I am trying to find an equation to match a 2D data-set (x,y) positions. I have X and I want to use an equation to predict Y to a rather accurate degree. As far as I can understand, I need to use some form of regression (non-linear, since the data is awfully curved). Now, I have no...

First off, thanks to the people who started this forum, and I apologize for this post being so long-winded. I'm a retired engineer dabbling in engine simulation. The text I'm using as the foundation for the gas dynamics theory contains several nonlinear equation sets for each simulated...

Hi everybody, could anyone help me in the linearization of the following non linear non-homogeneous ODE? A*dy/dt+B*y^(4)=C where A, B and C are constants. y is a function of t. is it possible to reduce this equation to a Riccati equation? do you know any analytical, approximate or...

Dear all, Apologies if this is in the wrong forum. I have a bit Nonlinear least squares fit problem. I have a pair of parametric equations (see attached, fairly nasty :frown: ). in it, a b c x0 y0 z0 are all constant, and they are the values I want to determine from a nonlinear least...

Hi, I'm a PhD student in Operations Management, and I've stumbled across a differential equation while modeling an OM concept. I was wondering if you could help me with this differential equation, or direct me in a way that would help me solve it. The equation is...

To the moderator: Please shift this to an appropriate forum, if necessary. Hi, I am solving a QM problem which requires using Mathematica to solve two equations, J_{\alpha}'(2\sqrt{\lambda}) = 0 (derivative of Bessel function) and J_{\alpha}(2\sqrt{\lambda}) = 0 (not simultaneously) where...

Is there any theorem or result which tells us whether a given set of nonlinar coupled differential equation (ordinary/partial) will have unique solution set? I need to know the answer for a second order ODE set. I understand there may be some difficulty since in this case the integration...

dear friends, i need to solve analitically(also by means of approximate methods) the following nonlinear differential equation: (A+BTs^(3))*dTs/dt+C*Ts^(4)=D where Ts is a function of t. A, B, C and D are costants. the initial condition is Ts(0)=Ti. I would be so grateful if anyone can...

Hello all, This is the first time I've stumbled across this site, but it appears to be extremely helpful. I am a meteorology grad student, and in my research, I have run across the following 2nd order non linear differential equation. It is of the form: y'' + a*y*y' + b*y=0 where a...

Homework Statement Solve the nonlinear system. x^2-2y^2=16 x^2+y^2=25 Homework Equations n/a? The Attempt at a Solution ive tried subtracting 1 equation from the other... (x^2-2y^2+9)=25 -(x^2+y^2)=25 -3y^2+9=25 -3y^2=16 y^2=-16/3 y=root of -16/3... im not even sure...

Any help with solving this first-order nonlinear ODE would be greatly appreciated! I do believe that an explicit solution exists. Homework Statement dy/dt = 1/(4t^2) + 1/2 + 1/2*y/t - 1/(2t)*((1+4ty)^(1/2)) I was led to believe that it could be solved by turning it into a linear...

Hi! I frequently have to solve systems of nonlinear equations with Fortran. So far I used a code which I didn't write by myself which is based on a Newtonian root finder from Numerical recipes. I would like to write a Fortran code on my own, based on another Numerical subroutine available on...

I am having trouble solving the following nonlinear first order differential equation: dy/dx = mx + b - k*y^2 The variables m, b and k are constants. I have had DE in school, but it was mostly linear first order, so I am not sure how to solve this one. Someone has recommended...

Homework Statement Solve the following for a_n in terms of x: a_{n+1} = \sqrt{x + a_n} Homework Equations The Attempt at a Solution Besides getting rid of the radical, I have no idea how to solve this.

Hello, What happens when phasor analysis is applied to nonlinear systems? could someone explain me how it would work? :confused: Thanks

Can someone explain to me what it means by nonlinear mode? I heard people saying that soliton is a nonlinear mode of the nonlinear schrondinger equation and therefore perturbed pulses tend to reshape to the soliton shape. In the reshaping proces, the energy dispersed is known as continuous...

Hi, I want to analyze a system of ODEs arising in biology of the form: x'=a1*x*z y'=b1*x + b2*y z'=c1 + c2*z + c3*y*z with x,y,z state variables and a1,b1,b2,c1,c2,c3 constant parameters. The difference to a linear system of diffs eqs. is that two state variables are multiplied...

[Differential equation at the end; All the intermediary stuff is the problem behind it.] I was curious about finding the velocity function for a free-falling object using solely Newton's equations. Using the force diagram, I've deduced that m-mass g-gravitational constant f_net - net...

I wasn't sure where to post this problem, as it's physics related, but rather advanced in its math content (and it's a problem for my applied math course). Homework Statement Considering a spring-mass system (like http://www.cs.toronto.edu/~faisal/teaching/notes/csc418/faisal/img/sm1.gif" )...

Hi all I am looking for different nonlinear control methods based on lyapunov theory. Indeed I should use a method which give the "region of attraction" explicitly such as CLF and Bakhstepping methods. Can enyone help me and introduce me some otehr methods? Many thanks in advance.

so I'm doing these lagrangian multipliers in calc class and it involves nonlinear systems and apparently the techniques I'm used to applying to linear systems aren't appropriate because i keep losing solutions, getting the wrong ones etc. so yea what are some efficient algorithms for this

I am sure most of you are familiar with the equation: m(x)''+c(x)'+k(x) = 0. Then, we create an auxillary equation that looks like this: mr^2+cr+k = 0. And, then we find the roots of this auxillary equation, calling them r1 and r2. And, if the roots are r1,r2>0 we consider the system to be...

is this equation linear or nonlinear?? Hello, I am a little bit confused.. Is the following equations linear or non linear: (dy/dt)^2+2y(t) = x(t). (here i don't know if (d^2y/dt^2) = (dy/dt)^2 ,if this is true then i know it's linear) dy/dt +(sin(t))y(t) = dx/dt +2x(t)...

Hi all. What do it mean by "slow variables" in NLS? I am reading a derivation of the NLS in the context of hydrodynamics, by R.S.John in his book "A modern introduction to the Mathematical Theory of Water Waves". In the book, slow variables are zeta = epsilon * (x-ct) and T = epsilon * t...

Hi all. I am a mechanical engineering entering the field of nonlinear wave. I am finding an introductory text on this topic. Things about nonlinear wave, nonliear optics etc. I would hope to get a really easy-to-read book first since I have actually NO prior experience in these fields AT ALL...

Suppose you have N unknowns and N NON-linear equations of those unknowns. Is it possible that the equations are LINEARLY-independent, yet you get an infinite number of solutions? I know the question of how many solutions you would get for a system of LINEAR equations is resolved with ranks of...

Could you give me an example of a function that satisfies scalar multiplication but not addition? more specifically, F: R^2 -> R such that F(av)=a F(v) but F(v1 + v2) != F(v1) + F(v2) The best thing I could come up with is F(x,y)= |x| . This obviously does not satisfy additivity, but...

Homework Statement Problem is presented as a nonlinear graph. Y-axis is in meters and ranges from 0.0 to 40.0m in increments of 10m, and the X-axis is in seconds, 0.0-5.0s (increments of 1). Points on graph include (0,10), (1,~19), (2, ~23), (3, ~26), (4, ~26), and (5, ~20). Question...

I have a single nonlinear differential equation like F(x2,dx1/dt,dx2/dt,d2x1/dt2,d2x2/dt2)=0 where x1=x1(t), x2=x2(t) i.e. a second order non-linear DE with no implicit dependence on x1(t). I suppose solving it results (in general) that one of the variables would be dependent on the...

Hi all, Can anyone please give me an example of a nonlinear differential equation used to model a certain type of circuit? Thanks

Hi all! I know that KdV is a balance of the nonlinearity and the dispersive effect and hence the wave profile propagates permenantly without disperse. However, why one always mention that it is the balance of WEAKLY nonlinear and WEAKLY dispersive? Can't it be a balance of STRONGLY nonlinear...

In the usual way to do QFT, we find the Green functions to the quadratic part of the lagrangian (usually with Feynman boundary conditions), and use this in the computation of n point (usually time ordered) correlation functions. Suppose one manages to solve instead the full nonlinear equation...

The Wikipedia article on Nonlinearity states: (emphasis theirs) Ref: http://en.wikipedia.org/wiki/Nonlinearity Interestingly, the page regarding http://en.wikipedia.org/wiki/Nonlinearity_%28disambiguation%29" states: (Not sure what "disproportionate" truly means here either.)...

I'm trying to find an algorithm to solve a 4 variable system of nonlinear equations.. the variables are named w,x,y,z and a,b,c,d are constants: a = x - y + z b = w + x c = y * z d = x * y / w Can anyone offer any advice? Much appreciated...

Hello All, I was doing some *basic* reading about nonlinear transmission lines and I was wondering what people make them out of? Is there a special nonlinear material that is used or does one simply use copper wire and caps and inductors? would it be possible to make one using simple coax cable...