Nonlinear Definition and 558 Threads

Hi I have a nonlinear equation for diffusion of multiphase fluids in porous media, and it is like 1/2(Laplacian(P^2)+d(p)/dy=d(p)/dt I couldn't find any analytical or semianalytical solution for this equation, do you have any idea?

Homework Statement I've started differential equations and I'm trying to understand the how to figure out if an equation is linear or not. The relevant equation I don't really understand either.Homework Equations http://img138.imageshack.us/img138/4158/8ac6f972e84a7e33c291f42.png The Attempt...

Hello everyone and thanks for looking at my thread, I had some trouble solving this ODE which was in a textbook by Henry J. Ricardo: x(e^y - y') = 2. This problem is from a section dealing with linear equations, but there is a hint beside the problem which reads, "Hint: Think of y as the...

i have problem to find the solution for : (3x3y+2xy+y3)+(x2+y2)dy/dx=0 i have tried the exact equation method : (3x3y+2xy+y3)dx+(x2+y2)dy=0 thus M(x,y)=(3x3y+2xy+y3) and N(x,y)= (x2+y2) then deltaM/deltay=3x3+2x+3y2 and deltaN/deltax=2x Since deltaM/deltay does not equal to...

i have to solve this equation : du/dx * du/dy = x*y u(x,y) = x for y =0 with putting this equation in the form : F(x,y,u,du/dx,du/dy) = 0 . it can be solved. But mine book does not explain how to do this, there are no examples. Can someone help me ? or any links of examples on the...

Hi, So I keep making mistakes trying to find all of the equilibrium points of different simple nonlinear systems. These problems aren't difficult, it's just that I keep taking different approaches to finding the equilibrium points. Is there a methodological way to know that I have found...

So, this is where I am stuck: ln\left(y\right)+y^{2} = \sin{x}+c_{0} I am confrused... :blushing:

i need help on this part, does anyone have any idead about maple lab? I should get the cure and trajectories in the red rectangular. But i try to fix the points and range, i still didn't get it http://img193.imageshack.us/img193/387/deqp.jpg trange1 := -3..3: window1 := x=1..3,y=-3..-1...

Anyone have any good online sources for nonlinear state-space modeling? I need to place nonlinear UAV dynamics into state-space form for modelling and seriously running out of good reference material for information.

Are the two words interchangeable?

Hi all, I have implemented a nonlinear lifting line method to estimate lift/induced drag of a typical wing. This method utilizes 2D lift coefficient data, and uses a numerical technique to solve the nonlinear equations. The program I have written in MATLAB is working, though I would like to...

Homework Statement Given the Second-order nonlinear ordinary differential equation x''(t)=1/(x(t)^2) Find x(t).Homework Equations I tried use Laplace transforms, and solving it using linear methods but that is not useful.The Attempt at a Solution I tried to find t(x) and got to...

Homework Statement Describe the phase portrait of the nonlinear system x' = x^2, y' = y^2 Also, find the equilibrium points and describe the behaviour of the associated linearized system. The Attempt at a Solution We have an equilibrium point at (0,0). The associated linearized...

A Nonlinear Second Order Differential Equation Problem: very frustrating please help! Hello, I am a first year engineering undergraduate student, and this is my question. Homework Statement A dust particle of negligible mass starts to fall, t=0, under the influence of gravitational force...

Homework Statement If I have a non linear integral equation of the form: y(s)+\int^x_0{K(x,s,y(s)}ds=f(x) and i want to find a way to solve this numerically using the Newton method Homework Equations The Attempt at a Solution after discretizing, and using the quadrature...

right now, my concept for their difference is that linear transformations are 1 to 1, where as nonlinear transformations are not. However, P^n to P^(-1) is a linear transformation, but it's not 1 to 1. the textbook def of linear transformation is that it must be closed under addition and...

I'm trying to solve the equation y'' = x^2 * y. This looks like it should be simple, but I don't have mathematica and the only reference I've found calls it a special case of the Emden-Fowler equation and refers to a solution in a book I don't own. Does anyone know the solution to this...

I've been told recently that the vacuum permittivity, given a sufficiently strong electric field, is not a constant, as it can cause positron-electron pair to split out of the vacuum. 1) is this true? 2) if so, where do such pairs as the positron-electron come from in a vacuum? I did try to...

Homework Statement Show whether or not the following transformation T is a linear transformation, given the description of T: T maps each point in R2 w/ polar coords. (r, θ) to R2 w/ polar coords. (r, 2θ). T maps zero-element to itself (T(0) = 0)Homework Equations I suppose (x, y) = (rcos(θ)...

the question is , can a delta function /distribution \delta (x-a) solve a NOnlinear problem of the form F(y,y',y'',x) the question is that in many cases you can NOT multiply a distribution by itself so you could not deal with Nonlinear terms such as (y)^{3} or yy'

Hi, I am solving the following nonlinear dynamical system using Energy Balance Method (EBM*). My intention is to arrive at an approximate analytical expression for the frequency of oscillation and the excitation force. u''+u=A(1+2*u) with u(0)=u'(0)=0, where A is a constant (Physically it...

Hi, I am looking for a nonlinear equation capable of approximating a sigmoid curve that can be multiplied by another equation of the same type with different parameters and this product can be made linear in the parameters. I am an ecologist, so I hope I am using the right terms. I...

I have to solve the nonlinear DE y'=x²-y² by using an infinite series expansion y=\sum_{n=0}^{\infty} a_n x^n, but I've tried in vain. Maybe a change of variables would make it easier, but I don't know which one. Thanks

Hi, I trying to solve a system of Nonlinear Differential Equations. I'm using Runge-Kutta on the Differential equations and Newton Method for the system. I have some doubts in how to create the JAcobian to the differential equations. Could somebody help me, please? Thank you, Aline

Haiya :P In the process of trying to find the solution of a 1st order PDE, I've reached a point where I have to solve the following ode: \frac{dy}{dx} = \frac{x^2y-4(y-x)^3}{xy^2+4(y-x)^3} and I am stuck here :( It's not separable, homogeneous, or exact and I...

Homework Statement I'm not sure if this is actually solvable, or a typo on my homework... but here's the problem in question: Solve the ODE: \frac{d^{2}y}{dt^{2}} + t^{2} \frac{dy}{dt} + y^{2} = 0, y(0)=0, y'(0)=0Attempt at solution I've been stumped on where to even start with this one, but...

Hi there, I hope my post is not against forum rules (not sure if this section is only intended for general questions or if it is ok to ask about specific problems .. it is definitely not Homework). Anyway, I was hoping that there were some guru's out there that can help me with the following...

Homework Statement solve the system of 3x^{2}+2y^{2}=35 and 4x^{2}-3y^{2}=24 Homework Equations The Attempt at a Solution I re arranged for y^2 and got 1\frac{1}{3}x^{2}-16=y^{2} I keep getting x to equal \pm 2.473 this is clearly wrong, the answers...

Hi, I need some help, I must solve the following nonlinear differential equation, -k1*(c'') = -k2*(c^0.5) - u*(c') subject to the bc, u*(c - 0.5) = k1*(c') where k1, k2, and u are constants, thanks

Why is it impossible to find ALL of einstein's equations in one place? well I suppose its irrelevant, I'd just like to know what math I have to do to define the energy-momentum tensor for a particle if I know say... its energy and momentum, or is that illegal? I'm struggling to grasp general...

Hello, I came across a somewhat special system of nonlinear algebraic equations which I think must have been the subject of consideration in some book or article. I failed however to find such a resource, so I hope you can help out and point me somewhere. The system consists of n equations and...

Homework Statement The stretch of a nonlinear spring by an amount x requires a force F given by: F=40x-6x^2 where F is in Newtons and x is in meters. What is the change in potential energy U when the spring is stretched 2m from its equilibrium position? Homework Equations U=.5kx^2...

Homework Statement http://www.math.udel.edu/~moulton/Apollo%20EC.pdf This is the full problem that I am working on for my ODE class. Homework Equations I would figure acceleration equals the second derivative so a=d^2s/dt^2 and V=ds/dt like the hint says. The Attempt at a Solution I...

Homework Statement Solve the nonlinear ODE du/dx=(u+x√(x^2+u^2 ))/(x-u√(x^2+u^2 )) by changing variables to x=rcos(theta), u=rsin(theta) and converting the equation to one for d(theta)/dr. The Attempt at a Solution Not sure if I'm going in the right direction. du/dx =...

Homework Statement We have the following x, y values x ||| y 1.0 -0.15 1.5 0.24 2.0 0.68 2.5 1.04 3.0 1.21 3.5 1.15 4.0 0.86 4.5 0.41 5.0 -0.08 How can you find the equation y(x) = ax^2 + bx + c by least squares? The Attempt at a Solution I know how to...

Homework Statement We recently discussed a problem in class involving free fall and parachutes.One of the examples was to solve for the area of a parachute in drag,gravity,air density,mass and the speed at which the object deployed the parachute and the speed it hit the ground out. I'm pretty...

I've recently been trying to solve the following equation: d2x/dt2 + (x2 - a) dx/dt + (x2 - b)x = 0 I've reduced it to a first order equation by a simple substitution of y = dx/dt to obtain: dy/dx = (a-x2) + [(b-x2)x]/y = 0 However I cannot figure out how to solve this equation. Is it...

Homework Statement This is just a nonlinear differential equation. All I have to do it solve it, though it is an initial value problem as well. 2*y*y' + y^{2} = t Initial value: y(0) = -1. The Attempt at a Solution This should be easy, but it doesn't seem easily...

how to solve a nonlinear system of algebraic equations such as : \sum^{m}_{i=1}x^{n}_{i}=k_{n} n=0,1,2... m<\infty \sum^{m}_{i=1}x^{n}_{i} is a power sum polynomial

Given the boundary value problem (primes denote differentiation w.r.t x): \begin{array}{l} y'' = f(x,y,y') \\ y(a) = \alpha \\ y(b) = \beta \\ \end{array} the nonlinear shooting method may be implemented to solve the problem. A bisection algorithm may be used or, with a little...

Hi. Could someone help me? In Boyd's book nonlinear optics equation 6.2.24 How to solve it? Basically, it is a 4 variables first order partial differential equation. How to solve it analytically? Thanks

[b]1. To solve for six unknown variables using six nonlinear equations using matrix form and to prooce it as singular. Tp1a_d,Tp2a_d,Tp1b_d,Tp2c_d, Tp3b_d,Tp3c_d are known variables Tp1,Tp2,Tp3, a,b,c are unknown variables. [b]2. Tp1a_d =Tp1+a*Tp1 Tp1b_d=Tp1+b*Tp1...

Hi All. Can somebody give me a sample MATLAB code for Newton-Raphson Method for Nonlinear 4x4 System of Equations. I'm trying to set a very ugly one up and haven't seen NR before the beginning of this week. I've figured the NR for a single eqn but this is driving me nuts.

Homework Statement Hi, i have the following system of equation. In the task is that system have periodic solution and have to be used polar coordinates. Homework Equations x'=1+y-x^2-y^2 y'=1-x-x^2-y^2 The Attempt at a Solution After transfer to polar system i tried to use the method...

Is this DE nonlinear? Homework Statement Determine the order and if this equation is Linear or Nonlinear. 3(d4x/dt4) + 4(dx/dt) + 9x = 3cos(3t) The d4x is a forth order derivative. Sorry for the messiness. Ok, this is a 4th order DE. I think it is nonlinear because of the two...

hi, i am facing problem in solving the following differential equation. help me. y''+ayy'+b=0, where y is a function of x, 'a' & 'b' are constants. i have tried substituting y'=u, which implies u'=u*dy/dx, these substitution change the equation to first order but i found no...

Is it accurate that general relativity may predict nonlinear but not chaotic spacetime?

1. Homework Statement + relevant equations I have to solve http://home.vs.moe.edu.sg/linl/eqn1.gif sigma, pinfinity, rho, N are constants. To make things easier for us, we are allowed to treat T as a constant. 2. The attempt at a solution Treat T as constant...

Hello, i am trying to solve this nonlinear ODE y'y''=-1 can someone help me? p.s maybe 2y'y''=-2 => (y'y')'=-2...

To the moderator: please move this to the section on differential equations if you think it would be better there. I'm looking at a reaction-diffusion equation of the form \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} + f(u), where, e.g., f(u) = u(1-u) for the...