Ode Definition and 1000 Threads

Homework Statement dy/dx= (4x sec(2y/x) +y) / x IC: y (1) = pi/4 Homework Equations The Attempt at a Solution So i can split that up into 4xsec(2y/x)/x +y/x = 4sec(2y/x) +y/x and let v= y/x dy/dx = xdv/dx +v 4sec(2v) +v = xv' +v 4sec(2v)=xv' which is...

I am working on the following Bernoulli ODE: 3xy^2 y' = 3x^4 + y^3. I come up with n = -2, so v = y^3 and y' = (1/3)v^(-2/3) v'. My integrating factor was x^-1. I end up with y^3 = X^2 + Cx yet the book has the same thing except X^4 instead of X^2. That makes me think I'm going wrong with...

So I am trying to figure out what substitution to use for the following ODE substitution: x^2*y' + 2xy = 5y^3; I initially moved the 2xy to the right but to no avail because when I tried to divide through by x^2 (to clear the left), I struggle to get the y/x format on the right. If the...

Hi, I recently need to do some numerical simulation by Euler method to solve a PDE. However, I noticed that there are some errors which are obtained with bigger numerical steps, when applying Euler scheme. Since my major is not mathematics, I do not know what this phenomenon is called. I...

x y'' + (x + 1) y' = 2 x Solve for y(x). Due to the coefficients being a function of x, I have no idea where to start to find the homogenous solution (Complementary Function). I know how to proceed after this part with the variation of parameters method. I just have no idea where to...

lets say there is a pond of 1,000,000 gallons of water. and the total of 10,000g of chemical is evenly dissolved in the water Fresh water starts pouring into the pond at the rate of 300 gallons/hour and the pond also releases water at the rate of 300 gallons/hour (hence no change in total...

Hi, well let me put the question a bit clear...my concern area is on ode and pde...my question is when you solve a pde/ode analytically and get a solution by asymptotic means does this mean that if solution exists then ...when using convergence as an alternative way of getting solution of the...

What is the difference between these two courses? ODE vs EDE? Hopefully this is the right place to ask. Does anyone know the difference between these two courses? And which one I should take? I'll be taking Linear Algebra (2nd semester of LA) with either one. I haven't decided which one to...

My math background is the Calc 1-3 series, and an intro to ODE class, but honestly I don't remember much from the ODE class (i started having to work during the time i had the class and just wound up cramming for tests and going in). I was feeling the same way about Calc 1 & 2 ( i took them...

Homework Statement y'(x)^2 = y^2 +xy Homework Equations hint : let u = y/x The Attempt at a Solution I divide x^2 on both sides and end up with... y'= y^2/x^2 + y/x then using the hint, i get y' = u^2 + u but i do not know how to solve the DE from here.

Hi to everyone, I have some problem in implementing a ODE system in matlab. function dC = Model(x,C) dC = zeros(2,1); dC(1) = -2/C(1) -3*dC(2); dC(2) = -3/C(2) -4*dC(1); [x,C] = ode23(@Model(x,C),[0 300],[56.9 0]); plot(x,C) The debugger says "? Input...

Homework Statement Show that the equation x= e^t converts the equation ax^{2}\frac{d^{2}y}{dx^{2}} + bx\frac{dy}{dx} + cy = 0 in which a,b,c are coefficients Homework Equations The Attempt at a Solution x = e^t and so does dx/dt. So you can write dx/dt = x using the chain rule dy/dx =...

Any one knows how do you call an equation of the type: y' = q_0(x)+q_1(x) y+...+q_n(x) y^n Maybe generalized RODE?

Can anyone tell me if this ODE has an analytic solution? And if it does, how the heck might I go about it? \left(\frac{1}{y^{2}}\frac{dy}{dx}\right)^{2}-\frac{A}{y^{3}}-\frac{B}{y^{2}}=D

Homework Statement Solve this system: x' = x + y² y' = -y The Attempt at a Solution My text solves this by guessing a particular solution. It says: For the second equation y' = -y yields y(t) = y_0(e^-t). Inserting thisinto the first equation, we must solve: x' = x +...

Hi I need to find the solution of d^2y/dx^2 + 2x(dy/dx) = 0 I've solved it in Maple and get that y=a*erf(x)+b but I have no idea how to arrive at this answer! Any help would be great, thanks.

What calc 3 topics will I need to learn before taking ODE? I'm going to be taking both at the same time and I want to know if there is stuff I need to be familiar with before starting. The class is using Fund of Differential Equations & BVP by Nagle (5th ed) and I have no syllabus yet.

Nonlinear 1st order ODE \frac{dH}{dt}=B-A*(H-Z)^{3/2} where: B,A and Z are known values H=f(t); H is function of t I've already solve this ODE numerically using a 4th order RK routine. But my question is, it is possible to get an analytical solution for H(t)?

hey guys, i was given some data points and i had to find an equation to fit the model. now my differential equation is h'= ah^b - ch^d with b < 0. I can't find any method for integrating because i don't know the constants in the equation. but i have the data points so that must help somehow. i...

Having a bit of trouble, what do i do next? Thanks.

Homework Statement \frac{dp}{dt} = \frac{d}{dt}\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}} = F Find v(t) show that v -> c as t -> infinity & find the distance traveled in time t if the object starts from rest. Homework Equations The Attempt at a Solution Ive tried rearranging it into either a...

The equation of motion of a rocket with mass depletion during ascent and subject to drag forces can be written as M(t) dV/dt = A - M(t)g - BV^2 (Eq. 1) with initial condition V(t=0) = 0 (V is velocity and t is time) Let us assume a linear mass depletion according to...

Homework Statement The Attempt at a Solution I did the "show that" part. But what is throwing me off is the x(0)=0 part. What is "x" a function of? Using the series in the square brackets, I found that when n=0, a_1 = a_0 ^2 n=1, a_2 = (a_1 * a_0)/2 n=2, a_3 = (a_0*a_2 + a_1^2 + a_2*a_0)/3...

Hi all, I have a 2nd order ODE I am trying to solve using NDSolve. In the ODE there are two constant coefficients and an initial condition that I want to 'vary'; meaning, I have a table of initial conditions with corresponding constant coefficients. It is straight forward to solve the ODE...

Homework Statement Find a general solution of the differential equation xy'' − (1 + x2 )y' = 0. Homework Equations Euler-Cauchy general form : xnyn+xn-1yn-1 ... +y=g(x) The Attempt at a Solution At first I tried using Euler-Cauchy but by multiplying by x (to get the x2 in front...

Hi, Could someone please show me how to solve the following simple problem using the Runge-Kutta (RK4) integration method? (tw')' + tw = 0 with w(0) = 1, w'(0) = 0 on the interval [0,1] by introducing the new variable v=tw' and considering the resulting first order differential system...

Hi, I'm having some trouble interpreting an equation. In Lamarsh's Introduction to Nuclear Engineering. The formulae for neutron attenuation is: I(x) = I_{0} exp(-\Sigma_{t} x I am given the formulae \frac{-dI}{I(x)} = \Sigma_{t} dx This formulae has been described as "the probability of a...

Hey guys, I am in dire need of help. In physics today, my professor gave us an experiment. It involved a strip of paper towel with dots along it from a sharp. it was hung from a metal ring stand and the edge of the paper towel was immersed into a dish of water. Water traveled up the paper towel...

The initial mass of fish in a lake was 7 thousand pounds on January 1st, 2001. Since the time, there was a 4-year moratorium on the harvesting on this specific type of fish. This species of fish reproduce at a rate proportional to the mass and by next year on the same date, there were 11.54...

Okay so registration is coming up and again its time for some tough decisions that will severely impact the upcoming months. I am currently an EE student taking Calc 2 and Physics I. Next semester I was planning on doing Calc 3 and Physics 2 and in the summer taking ODE and Circuit analysis...

Homework Statement Find the general solution to x'' + e^(-2t)x = 0, where '' = d2/dt2 Homework Equations - The Attempt at a Solution First I did a change of variables: Let u = e^(-t) Then du/dt = -e^(-t) dx/dt = dx/du*du/dt = -e^(-t)*dx/du d2x/dt2 = d/du(dx/dt)du/dt =...

Homework Statement one duck is situated in each of the four corners of a 2mx2m square pen. suddenly, each duck begins to chase its anticlockwise neighbour. all the ducks travel at the same speed. (a) by defining the origin of an x-y coordinate system in the bottom left hand corner of the...

Homework Statement y''(x-1)-xy'+y=x2-2x+1 The Attempt at a Solution I don't even know how to start this, Don't know what substitution to do.

I struggle to solve this Differential equation: x^2y' +2xy = arctanx What I did was just divide x^2 on both side of the sign of equality in order to get the same form as a first-order linear diff.equation. After I've done that, I just multiply e^(2lnx) on the both side of the equation so...

Hi, have this strange 2nd order ODE in one of my tutorials that I am struggling to start. I am not used to dealing with derivatives of both x and y as well as a function involving t. I was wondering if anyone may be able to point me to the starting line. I am trying to convert them into 1st...

Every second order linear ODE a(x)y''+b(x)y'+c(x)y=F(x) can be transformed into the forms; u''+g(x)u=h(x) divide whole equation to a(x) and choose y(x)=u(x)^(e^s(x)) but how i choose s(x) ?Please help...

Hi, I have a coupled system of ODE like: w1'' = A w2'' + B w1 + C w2 w2'' = D w1'' + E w1 + F w2 I need to solve it analytically but it seems it cannot be solved using eigenvalue method. My concern is first that if this system have sufficient equations and if so how it can be solved...

Hi, I posted this on the homework forum, but I haven't gotten any responses there. I thought there might be a better chance here. 1. Homework Statement I have the ODE h'' + h'/r + λ2h = 1, where h = h(r), and I want to find h(r). 2. Homework Equations The corresponding...

I have a third order, non-linear, homogeneous, constant coefficient ODE that I need to solve but have no idea how to do it. To make matters worse, one of the boundary conditions are indefinite. Here's the equation, y''' + y*y'' - y'^2 + 1 = 0 and the BC's y(0) = 0 y'(0) = 0 y'(\infty) =...

Homework Statement A car, of mass 720kg, moves along a straight horizontal road. The engine of the car exerts a constant power of 81kW. The car experiences a resistance to motion which has magnitude 90v N, where v ms^-1 is the speed of the car at time t s (a) Show that v satisfies the...

Hi 2 all Necessary i need ode that's have no general sol nd I need also an ode that's i can solve it with more way i hope 2 found it .. thanks all i w8

I attached scans of the questions rather that typing it all here. It's also easier to read. Questions: http://img4.imageshack.us/img4/9306/33991727.th.jpg Attached Reference Materials: http://img40.imageshack.us/img40/6599/74821170.th.jpg

Homework Statement Find a continuous y(t) for t > 0 to the initial value prob: y'(t)+p(t)y(t)=0, y(0)=1 where p(t)=2 for 0 < t < 1 p(t)=1 for t > 1 and determine if the soln is unique. The Attempt at a Solution By standard ODE techniques I arrive at y=\exp(-2t) for 0 < t < 1 y=\exp(-t)...

Homework Statement Use a Green's function to solve: u" + 2u' + u = e-x with u(0) = 0 and u(1) = 1 on 0\leqx\leq1 Homework Equations This from the lecture notes in my course: The Attempt at a Solution Solving for the homogeneous equation first: u" + 2u' + u = 0...

Solve using laplace. The diff eq is y'' + 2*y' + *y = 0 subject to y(0)=1 and y(pi)=0 Sorry if notation isn't the norm. y'' and y' and y are time (t) based functions.

Homework Statement y'(t) = (y-5t)/(y+t) IVP: y(1)=0 Homework Equations M(x,y)dx+N(x,y)dy = 0 - or do i use - y'+p(x)y=q(x) The Attempt at a Solution Well I used the first equation (with M and N): 1. first checked that it was exact, by taking the partial of M and N with respect to y and t...

Given the equation y'= xg(x,y) , suppose that g and (partial) dg/dy are defined and continuous for all (x,y). Show the following: 1) y(x)=0 is a solution 2)if y=y(x), x in (a,b) is a solution and if y(x0)>0, x0 in (a,b), then y(x)>0 for all x in (a,b) Please i need your help.

Homework Statement A curved mirror of equation y=y(x) has that property that whenever a ray of light emanates from the origin it reflects parallel to the x-axis. Find the equation of the mirror Don't even know how to get started on this, Don't need a solution just need some starting hints...

Homework Statement dx/dt = x - y + (x^2) - xy dy/dt = -y + (x^2) - Determine the critical points for the equation, - Determine the linearized system for each critical point and discuss whether it can be used to approximate the behaviour of the non-linear system. What is the type and...

Homework Statement I'm working with a heat equation that requires a Laplace transform. I performed the transform and ended up with a basic ODE with a particular solution. I solved for the particular solution and then realized I was working on an infinite domain in my spatial dimension...