Nonlinear differential Definition and 65 Threads

Using the null geodesic and the Schwarzschild metric, this differential equation for photon trajectory near a mass can be derived, where u is r_s /2r: Though this nonlinear ode is fairly easy to approximate (which I already have), I'm looking for an analytic solution or an approximate...

hi, i am working on nonlinear differential equation- i know rules which decide the equation to be nonlinear - but i want an answer by which i can satisfy a lay man that why the word nonlinear is used. it is easy to explain nonlinearity in case of simple equation i.e when output is not...

The equation is as attached where, - α, β and γ are constants - i1 and i2 are the variables. Also attached, is my attempt and where I stuck at. If anyone has an idea how to convert this into Bernoulli’s form, please I really need help. If there are any other ideas please let me know too...

That's pretty much it. If there is a very basic strategy that I am forgetting from ODEs, please let me know, though I don't recall any strategies for nonlinear second order equations. I've tried looking up "motion of a free falling object" with various specifications to try to get the solution...

Hi there can someone please help me with this differential equation, I'm having trouble solving it $$ \begin{cases} y''(t)=-\frac{y(t)}{||y(t)||^3} \ , \forall t >0 \\ y(0)= \Big(\begin{matrix} 1\\0\end{matrix} \Big) \ \text{and} \ y'(0)= \Big(\begin{matrix} 0\\1\end{matrix} \Big)\end{cases}...

Homework Statement: first order non linear equation Homework Equations: dT/dt=a-bT-Z[1/(1+vt)^2]-uT^4 a,b,z,v,u are constant t0=0 , T=T0 Hi, i need find an experession of T as function of t from this first order nonlinear equation: dT/dt=a-bT-Z[1/(1+vt)^2]-uT^4 a,b,z,v,u are constant...

Homework Statement Hi, I'm trying to calculate the formula for the position vs. time of a rocket landing from an altitude of 100km. I'm neglecting a lot of forces for simplification but basically, I want to solve ##F_{net} = Drag - mg##. Homework Equations Drag Force: D = ## \frac {C_dAρv^2}...

The term 'phase space' is often used in the study of nonlinear dynamics.What is it.

Homework Statement Consider the Kortweg-de Vires Equation in the form $$\frac{\partial \psi}{\partial t}+\frac{\partial^3 \psi}{\partial x^3}+6\psi\frac{\partial \psi}{\partial x}=0$$ Find the relation between the coefficients ##c## and ##d## , such that the following quantity is conserved...

ρCp (∂T/∂t) + k (∂2T/∂x2) = exp(-σt2)exp(-λx2)φo i have this equation... i was thinking of taylor series expansion to solve it and make it easier... any ideas on how to solve?

Hello every one, I have an equation related to my research. I wonder if anyone has any suggestion about solving it? y''+y' f(y)+g(y)=h(x) thanks

I need to solve the well known momentum equation in 3D cylindrical coordinates: ρ(∂v/∂t +(v.∇)v)=A where A and the velocity v are both local vector variables. I am actually looking for the stationary solution to the equation, i.e. no ∂/∂t term) I have tried evolving the velocity and tried...

Homework Statement I need to solve the follwing differential equation $$(\frac{df}{dt}) \dfrac{4 n e^{4nf(t)}-9n e^{2nf(t)} (\frac{df}{dt})^2 + e^{2nf(t)} r^2 \frac{d^2f}{dt^2}+5n (\frac{df}{dt})^4 r^4 - r^4 \frac{d^2f}{dt^2} (\frac{df}{dt})^2}{-e^{2nf(t)}+ (\frac{df}{dt})^2 r^2}=0 $$...

Good evening I have these coupled equations and was wondering if there is any chance solving them analytically. If not, how would you approach it numerically? (shown in attachment) Thank you very much

how do you solve this equation? y´´ + k/(y^2) = 0 ? I got it from applying Newton's 2nd law of motion to an object falling from space to Earth only affected by gravitational force. Thank you!

I need to find a trapping region for the next nonlinear ODE system $u'=-u+v*u^2$ $v'=b-v*u^2$ for $b>0$. What theory i need to use or which code in Mathematica o Matlab could help me to find the optimal trapping region.

Hello I have a system of differntial equations: dx/ds = sin(p) dy/ds=cos(p) dp/ds = k dk/ds = -1/EI(s)*(k*dEI/ds+f*sin(p)) x(0)=y(0)=p(0)=p(L)-pl = 0 These are nonlinear differential equations. I should use some sort of nonlinear finite difference. But I do struggle to setting up the finite...

i want to solve a nonlinear PDE with finite difference method ,but using just discretization like in linear PDE , it will lead to nowhere , what's the right way to use FDM to solve nonlinear PDE or could someone provide me with book's titles or articles that can help me solving a nonlinear pdf...

Hello, I'm a doctoral student in civil engineering. In my research I came across a differential equation for the net force acting on an object as it impacts a granular medium at low velocities. z'' + a[ z' ]^2 + b[ z ] = c Where a, b, and c are all constants I believe that this equation will...

In my introductory ODE class we have focused mostly on linear differential equations. I know that nonlinear differential equations are much harder to solve, and I am wondering what exactly the "state of the art" methods are for dealing with them, or also what recent developments have been made...

Homework Statement By truncating the differential equation below at n=12, derive the form of the solution, obtaining expressions for all the ancoefficients in terms of the parameter \lambda .Homework Equations The ODE is: \frac{\mathrm{d^2}\phi }{\mathrm{d} x^2} = \frac{\phi^{3/2}}{x^{1/2}}...

This is part of a personal project... I've recently become addicted to modeling various physical systems from scratch, such that I find explicit solutions of position as a function of time, and graph em. But I've hit a glass ceiling trying to find an analytic solution to the 1-dimensional...

Hi, I need help solving this ode, when I try to solve it I end up with a big crazy answer and I believe it should be simpler. (dy/dx)^2=((ay^4)/2)-(a+1)y^2+1 y(0)=0, y'(0)=1 and a is within [0,1]

Solve the 2nd order nonlinear differential equation, with initial conditions y(0)=0 and y'(0)=1 y''=2ay^3-(a+1)y with a within [0,1] I am pretty much lost on how to go about solving this. It would be greatly appreciated if someone could point me in the right direction on this. Thanks!

Hi everyone, I need some help to solve this differential equation. The question states "Use the perturbation or multiple scale method to find the third-order approximate solution for the following system: diff(x(t), t, t)+w^2*x(t)*(1+epsilon*x(t)^2) = 0 " Currently, I am still...

dy/dx=2x+y^2 By the way, methods of solving linear differential equation are useless, such as integrating factor and Bernoulli method.

Take for example a system \frac{dx_i}{dt}=(x_i,t,a,b,...) i-number of state equations. What would be the maximum number of parameters permitted for this system of non-linear differential equations? Is it finally determined by the solution space?Is there a criteria for number of...

Homework Statement How do you derive the time-dependent velocity equation for motion along a curve, such as a skateboarder on a half pipe? For the sake of abstraction, I ask myself the following: A uniform sphere of mass m and radius r is set free from the top edge of a semicircle half pipe...

I saw this post at stackexchange: I ran across this post when trying to solve a homework problem. But I have no idea how he got that solution for that. When I use the Euler-Lagrange, I get this diff eq below. Here is the simplest form I have managed to get it in...

Homework Statement Is this differential equation linear or nonlinear? Assume that y' means dy/dx. Homework Equations 1. Homework Statement [/b] Is this differential equation linear or nonlinear? Assume that y' means dy/dx. Homework Equations \sqrt{xy'+2x2}=5 The Attempt...

Hi, Part of my research, I nondimensionalized an ODE to eventually arrive at this form: sin(τλ) = q^((n+2)/(n+1)) + κq' + q'' where q' = dq/dτ The problem is of course the nonlinear q^n. n is an integer greater than 0. Is there a Laplace transform for this? Or what solutions are there for...

I've been reading through my mechanics of materials textbook recently, notably in regard to the section on the deflection of beams. The well regarded Euler-Bernoulli beam theory relates the radius of curvature for the beam to the internal bending moment and flexural rigidity. However the theory...

Hey, I need your help to solve the following set of coupled differential equations numerically. dn(t,z)/dt=I^5(t,z)+I(t,z)*n(t,z) dI(t,z)/dz=I^5(t,z)-α(n(t,z))*I(t,z) where I(t,0)=I0*exp(-4ln2(t/Δt)^2) and n(t,0)=0 and n(-certrain time,z)=0. Some constant parameters I did not show...

Homework Statement Consider the following differential equation: x^{2}\frac{dy}{dx}=x^{2}-xy+y^{2} State whether this equation is linear or nonlinear and find all it's solutions Homework Equations I think that the Bernoulli differential equation is relevant, but I'm not sure...

Is it possible to solve the following differential equation analytically? y''(x) = A - B [exp(y(x)/C) - 1] where A, B and C are constants. Thank you...

Homework Statement In one problem I had got to this equations, but I was not able to solve it, because I'm actually on high school. The equation : d^2/dt^2(x) = -h*g/(h+x) I tried use separation of variables but I was not able to use the chain rule. Can anybody show me the steps...

Hello to everybody, I'm very new to solving ODES and equations with MATLAB. I have been asked to solve a system of nonlinear equations for simulating the growth of a solid tumor. Assuming that we have the 5 unknowns which are dxd arrays: f,g,m,p and n. f(x,t) is the volume fraction of tumor...

Hi, I need some help to find the analytical solution of the following DE: x" - k x/x' = at + b, with x' = dx/dt and x" = d(dx/dt)/dt Any kind oh help or advices on where I can find some useful resources are really appreciated. Thank you

Homework Statement Find the orthogonal trajectories of the given families of curves. x^2 + y^2+2Cy=1 Homework Equations The book has covered homogeneous and separable methods.The Attempt at a Solution To find the orthogonal trajectories, we simply find the curves whose tangents are...

Hi All, I have been trying to solve following nonlinear differential equation, but I couldn't solve it. 0 = a*[f(t)]^{z/(z-1)} + (-t+C)*f(t) + b*[df(t)/dt] where a, b and C are constants and 0< z<1. Could you please help me how to solve this nonlinear differential equation? I would...

I've been trying to solve this one for a while. My professor wasn't even sure how to do it. Any suggestions? y''+t*y+y*y'=sin(t)

Homework Statement The following equation turned up while I was trying to make an integral stationary in a 'calculus of variations' problem. y^{\prime}(x)^2 + 1 = y^{\prime\prime}(x) y(x) How would one go about solving this nonlinear equation?

Homework Statement y+4y^2=(y^(4)+x)y', IC: y(1)=1 Homework Equations ? The Attempt at a Solution Ive tried to figure out a substitution that will make this linear, and i can't seem to figure one... I am unsure of how to approach this?

this is the problem: x2y' = (2y2 - x2) here's what i have done so far: dy = (2y2/x2 - 1)dx (2y2/x2 - 1)dx - dy = 0 i used the substitution y = xv then found an integrating factor and got dx/x - dv/(2v2 - 2v - 1) = 0 but i am stuck at this point.. i know ln(x) + C is the first part...

Homework Statement y''+4\left(y'\right)^{2}+8=0 Homework Equations u=y'? The Attempt at a Solution I don't really know where to start, do I use u=y' substituted? So, y''=u*(du/dy)? That leads to u\frac{du}{dy}+4u^{2}+8=0 I don't think this is correct, since it leads to...

Hello everybody, could you please direct me how to solve this nonlinear differential equation analytically, so by mathematica or matlab? I really need to solve it for my research project, so please help me du/dx=d/dx[a*u^(-1/2)*du/dx]-n*u^(3/2)*(u-c)/b boundry conditions are: u(0)=b+c...

-f''-(2/x)f'+(2/x^2)f+f^3-f=0 the boundary condition is f(x=0)=0 and f(x=\infty)=1 how to solve f numerically?

Hello, Can you give some suggestions to solve the following system of 1st order nonlinear differential equations? Thank you. \[ \begin{array}{l} u'(t) = Au^2 (t) + B(t)u + C(t) \\ u(t) = \left[ {\begin{array}{*{20}c} {x_1 (t)} \\ {x_2 (t)} \\ \end{array}} \right] \\ A = \left[...

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

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...