Differential equations Definition and 999 Threads

hello to everyone, I have a problem solving a stochastic differential equation of the form: dX/dt=aX²+bX+c+sXn(t), where n(t) is white noise with a mean value equal to 0 and variance equal to one. Does anyone know the solution of this stochastic differential equation or how to solve...

How do the "d" terms in differential equations work? Hi, I was hoping someone could explain how the "d" terms in differential equations work? For example, d2y/dx2 = 4x3 +1 To solve I have been rearranging to get, d2y = (4x3 +1)dx2 and then doing a double integral of each side...

Hi, I am trying to solve the two equations cited below but not sure if it is possible to solve them... ∂(yv)/∂t=f(y,v,t) where v is velocity = dx/dt, and y is a material property. In addition: ∂v/∂x = constant Any hints would be appreciated. Many Thanks!

Hello! I am trying to solve two differential, non-linear equations in C# using fourth-order Runge-Kutha method. I implemented them in C#: private const int ALFA = 7600; private const int MU = 7200; private int BETA =...

hi , can anybody give me some examples of 'systems of linear differential equations with periodic coefficients'? i don't know how to solve it.. where can i get problems and solutions on this?

Anyone have a great recommendation for a textbook on 1st semester/year/undergraduate differential equations? I would like for: 1. The books style to cater to auto-didactic learning. 2. Emphasis on engineering problems/applications and/or emphasis towards engineering students. (i.e. non-math...

Hello, all: I have a few questions concerning a definite integral where I am meeting with limited success. The most important problem concerns: \int_{0}^{\infty}\frac{\cos{x}}{x^2+1}dx Contour integration always has been my last resort, but differentiating under the integral sign, I soon...

I'm not sure if this should go in this section or the learning materials section, so please feel free to move this thread to the appropriate location. This semester I am taking differential equations. I have a totally awesome professor :) So far we have been working on linear algebra and...

I'm trying to figure out which set of differential equations describe the following quite general but relatively simple system: A chamber which volume can be changed by moving a piston filled with a gas. Additionally, gas can be released from the chamber through a relief valve and heat can be...

So in Griffith's (ed. 2 page 37) there's an equation that says that **pretend the h's are h-bars...I don't know Latex very well** ih\frac{1}{\varphi}\frac{d\varphi}{dt}=-\frac{h^{2}}{2m}\frac{1}{\psi}\frac{d^{2}\psi}{dx^{2}}+V Since in this simplified case V where is a function of x alone...

Homework Statement 20) Determine the general solution of y'' + y = sin(x). Homework Equations The Attempt at a Solution We attempt to solve this equation by the method of undetermined constants. So y = u(x)sin(x) (such a substitution should reduce R(x) to a polynomial with a u-differential...

Hi Homework Statement y'=(y-x)^{2} Homework Equations The Attempt at a Solution I have nearly no idea in order to solve this solution. One hint is given: We shall find a new variable which makes it possible to separate the differential equation afterwards. I'm not sure...

1. x' + y' - x = -2t x' + y' - 3x -y = t^2 2. x' = Dx, y' = Dy 3. I eliminated x to get y alone by multiplying the first row by (D-3) and the second row by (D-1) (D-1)(D-3)x + (D-3)Dy = -2t(D-3) (D-1)(D-3)x + (D-1)(D-1) = t^2(D-1) then subtracted to get: (D+1)y =...

Hi all. Woohoo, I'm in diff eq now. Gosh, I've been on this board since Calculus I think. Sorry I usually only come around when I have a question. :\ Sooooo, Thursday my professor did an example of solving a system of linear differential equations with using the linear operator D...

Homework Statement here is the circuit >>> http://www.4shared.com/photo/F3ewfm_3/22_online.html the whole question is here >>> http://www.4shared.com/document/Qwxgzq78/Circuits_for_Modeling.html whats assigned to me is #22. anyways, what we need to get here is the differential equations...

I am trying to solve an IVP problem and I seem to be stuck on it because I am getting an integration that seems very complicated and I think I messed up on it, I have my work so far below. Homework Statement Find the solution to the IVP ty^'+7y=2t^2 e^2t, y(1)=7 Is this equation...

Homework Statement I don't know how to type math equations of I have included a image file. Take initial conditiona as [0 1] Homework Equations The Attempt at a Solution No idea

I have two systems of linear differential equations: \frac{dx}{dt}=Ax, \frac{dy}{dt}=By x,y are vectors of length n and A,B are nxn matrices. I have a third system defined by: \frac{dz}{dt}=-ABz Is there anything we can say about what the third system represents in terms of the first two? If...

Homework Statement Find a differential equation whose solution is a family of circles with centers in the xy-plane and of variable radii. Hint: Write the equation of the family as x^2+y^2-2ax-2by+2c=0 Homework Equations The previous questions asks to find a differential equation whose...

Homework Statement Suppose the rate at which the volume in a tank decreases is proportional to the square root of the volume present. The tank initially contains 25 gallons, but has 20.25 gallons after 3 minutes. Solve for the general solution (do not solve for V). The Attempt at a...

Homework Statement The current I(t) in an electrical circuit satisfies the second-order differential equation 2Ϊ + 3İ + I = 0. Find the solution I(t) of this equation which also satisfies the initial conditions I(0) = 1, İ(0) = 0. Homework Equations a((d^2y)/(dx^2)) + b(dy/dx) + cy = 0...

Homework Statement Suppse dn/dt = 1/10n and n(1)=-2. Separate the differential equation, then integrate both sides. The Attempt at a Solution How do I do this? There is no 't' to 'separate' from the equation. Would it just be: int[1/10n] = int[0t] ?

I have the following equation:: xy' = y + 2*sqrt(xy) I know I should either use the F(y/x) substitute or Bernoulli's method of substitution but I'm not sure how to manipulate the equation to determine which it is. If someone had some helpful tips on how to start, please let me know...

Okay, in the Escape Velocity Equation, with the usual notations, v2=2gR2/r + (v02-2gR) a few articles like [PLAIN]"www.math.binghamton.edu/erik/teaching/02-separable.pdf"[/URL]give the following explanation: ... ... ...(implying that v0>=√2gR) That raises a few doubts in my mind...

The local university offers both partial differential equations and higher geometry I (both of which seem equally interesting to me!), but they are only offered during the same time! As I'm most likely going to major in physics when I go to college, which class would have more applications to...

hello, i just want to ask if mathematica 7 can solve nonlinear second order partial differential equations. i tried solving it with DSolve but it kept on giving me the question back as the output...please is there any way or syntax for solving it on mathematica 7?...thanks for any suggestions.

One solution of the differential equation x^2(x^2+1)y^{\prime\prime} - 2x^3 y^{\prime} + 2(x^2-1) y = 0 can be obtained in the form y_1 = x^n. Use this solution to find another, and in this way find the general solution. The DE can be written as: \displaystyle y^{\prime\prime} -...

Homework Statement So I have two problems that ask me to separate variables: 1: du/dx * x(x+1) = u^2 u(1)=1 2: dy/dt=y(2-y) Initial condition y(0)=1 The Attempt at a Solution For #1 i get each variable on one side and have integral(u^-2du)=integral(dx/x(x+1) I use partial...

Homework Statement m\frac{d^{2}x}{dt^{2}}+c\frac{dx}{dt}+kx=F_{0}cos\omega t\\ LC\frac{d^{2}V_{c}}{dt^{2}}+RC\frac{dV_{c}}{dt}+V_{c}=V_{0}cos\omega t These two equations are for two different physical phenomena. The first is for a mass moving along an x axis. The mass is affected by a...

Homework Statement [PLAIN]http://img220.imageshack.us/img220/7427/diff5.jpg The Attempt at a Solution Done (a). How do I go about (b) and (c)?

Find the general solution to: dy/dx = 3x2y I tried saying u = 3x2 and v = y then du/dv = 6x and dv/dy = 1 and get 3x2 + 6xy but now i think iv gone completely the wrong way around this . . . .

Homework Statement [PLAIN]http://img402.imageshack.us/img402/7427/diff5.jpg The Attempt at a Solution How do I evaluate \frac{d}{dx} \left( \frac{y_2}{y_1} \right) ?

Hi, I'm trying to solve the following coupled PDE's u_{tt}-gHu_{xx} - gHv_{xy} = -2\frac{g^2}{\omega} \left\{k\frac{\partial^2 |A|^2}{\partial x^2} + \ell \frac{\partial^2 |A|^2}{\partial x\partial y} \right\} v_{tt}-gHv_{yy}- gHu_{xy} = -2\frac{g^2}{\omega} \left\{ \ell\frac{\partial^2...

Homework Statement Model the following reaction with any software. You have a gas phase reaction going on at the wall of a catalytic reactor. Homework Equations dA/dx = f1(x)*(A-B) dC/dx = f2(x)*(C-D) f1(x)*(A-B) = Const1*(D/1+D)*B f2(x)*(C-D) = Const2*(D/1+D)*B The Attempt at a Solution i...

I have the equations \frac{l}{u^{2}} \frac{du}{dx}=constant and \frac{1}{u} \frac{dl}{dx}=constant. By "eyeball", I can say the solution is l \propto x^{n} \ and \ u \propto x^{n-1}. I can't see how I could arrive at these solutions 'properly', if you know what I mean

I am currently taking calculus, and will be done with differential equations by the time I graduate high school, maybe by junior year. I was wondering what comes after differential equations, because up to differential equations there was a series of maths that you were supposed to take...

Homework Statement Hi there. Well, I have some doubts about this exercise, I think I've solved it, but I wanted your opinion, which always help. So, it says: There is no general method for solving the homogeneous general equation of second order y''+P(x)y'+Q(x)y=0 (1) But if we already know a...

Hi, I'm half way through a piece of differential equations coursework and I'm having serious trouble with a couple of things. The brief of the coursework is to investigate the effects of air resistance on falling objects by conducting an experiment to obtain a set of results, then using...

What to take first? Much help would be appreciated: Just took calc 1 and discrete mathematics.

Homework Statement solve the equation dy/dx = y/x Homework Equations The Attempt at a Solution dy/dx = y/x dy/y = dx/x lny = lnx + c my book gives the answer y = kx not sure how they got that, did they just take the log of the constant, because its just...

Could somebody help me to solve this really tough differential equations? \left( {x}{y} \sqrt{{x}^{2} - {y}^{2}}+{x} \right){y'}={y}-{x}^{2} \sqrt{{x}^{2}-{y}^{2}} Another tough one.I tried MATLAB which gave me sth about lambertW function which I haven't heard about before.Is there an...

Homework Statement We are working on homework for a population model affected by an endemic disease (smallpox). There are 3 types of individuals in the population, S (susceptible), I (infected), and R (recovered). Homework Equations The total population N = S+ I + R. The three differential...

Are all linear differential equations considered linear systems? Does the "linear" in both terms reference to the same characteristics? http://en.wikipedia.org/wiki/Linear_system http://en.wikipedia.org/wiki/Linear_differential_equation

Does the variable coeffcient in linear differential equations have to be polynomials? All the examples I have found seem to be polynomials for example the Cauchy–Euler equation. For example is sin(x)y'' + cos(x^2)y' + y = 0 still considered a linear differential equation with variable...

The original form: http://img190.imageshack.us/i/79624585.png/ http://img685.imageshack.us/i/70092098.png/ I have manged to get to (D + 1)x + (D2 +D +1)z = 0 but after that I am kind of lost.

Homework Statement a) What can you say about a solution of the equation y' = -y^2 just by looking at the differential equation? b) Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a) c) Can you think of a solution of the differential equation y' =...

Homework Statement Given a second order differential equation: y'' + P(x)y' + Q(x)y = 0 If y1(x) and y2(x) are linearly independent solutions of the DE, what form does Abel's Equation give for W(y1(x), y2(x))? If we assume that one solution y1(x) is known, what first order DE results from a...

Homework Statement "Show that each of the given differential equations of the form M(x,y)dx + N(x,y)dy = 0 are exact, and then find their general solution using integrating factors μ(x) = e∫h(x)dx and μ(x) = e∫g(y)dy Homework Equations (x2 + y2 + x)dx + (xy)dy = 0The Attempt at a Solution...

Homework Statement I don't have a homework question. I have more of a general question. Let's say we have a solution... x=C1*[a1 a2]^{T}*e^{lamda1*t} + C2*[b1 b2]^{T}*e^{lamda2*t} As t approaches infinity how do you determine what the solution does? Homework Equations...

Is there any software packages available to solve Differential equations(first order and second order)? This will be great help for me.