Ode Definition and 1000 Threads

Homework Statement xy'-(x+2)y=-2x2-2x Homework Equations The Attempt at a Solution I'm clueless as to how to solve this as I'm only experienced in using the power series method with homogenous ODE's. Even if I make this homogenous, I don't know what to do with the x-variables that are not...

I need to solve the following ODE \frac{dy}{dx}=\frac{x(1-x^2)+ky^2}{y} I don't know what is the correct method to use though. Any help would be brilliant, thanks.

First, I looked for a MATLAB forum here but didn't see one so if there is and I missed it let me know for future posts I have a few more questions. Second, this isn't ode related but plays a small part in the next, longer question. This is two parts: I have an i7 980x w/12GB of RAM 2 gtx 295s...

Homework Statement Find a general solution. Homework Equations 2x\frac{dy}{dx}+y^{3}e^{-2x}=2xy The Attempt at a Solution Looks like a Bernoulli equation to me, after some algebra: \frac{dy}{dx}+\frac{y^{3}}{2xe^{2x}}=y \frac{dy}{dx}+\frac{y}{2xe^{2x}}=y^{-1} so with...

I would appreciate any advice on the following ODE substitution question: xy' = y + (x^2 + y^2)^.5 Dividing thru by x and using the usual y/x substitution, I get: y' = v + (1 + v^2)^.5 but I don't know if that is right or how to integrate the left side. The book has the answer of y + (x^2 +...

I have the following logistics problem that I am stuck about halfway thru: The time rate of change of a rabbit population P is proportional to the square root of P. At time t=0 (months) the population numbers 100 rabbits and is increasing at the rate of 20 rabbits per month. How many rabbits...

So I have the following Bernoulli ODE: x^2*y' + 2xy = 5y^3 I use an integrating factor of x^-4, my n value is 3. I am okay until I get to the very end, where I get y^-2 = (2+Cx^5)/x; the book shows y^2 = x/(2+Cx^5). Am I must missing an algebra step or did I make a mistake somewhere within?

Homework Statement Solve ODE of form y''+(2/x)y'=C*(e^y) where C is a constant Homework Equations The Attempt at a Solution I don't really see how to approach this one, so a point in the right direction would be great. Thanks,

Homework Statement Find a general solutionHomework Equations (x+y)\frac{dy}{dx} = x-y The Attempt at a Solution \frac{dy}{dx} = \frac{x-y}{x+y} let v=y/x y=xv \frac{dy}{dx} = v+x\frac{dv}{dx} now, v+x\frac{dv}{dx} = \frac{x-xv}{x+xv} = \frac{1-v}{1+v} = \frac{1}{1+v} -...

I know that the rate of change with time of a population is proportional to the square root of t. T=0 is y = 100. Population increases at rate of 20 per month. I started out by trying to do dy/dt = p^.5. I am used to the population problems where I use y=Ce^(rt) but am having trouble...

Tank w/ 100 gal pure water. At time = 0, sugar/water mixture with .2 lbs of sugar per gallon enters at 3 gal/ minute. Drain opened at bottom allows sugar solution to leave at 3 gal per minute. Perfect (lol) mixing occurs. I show the following: Rate in: .2 x 3 = .6 Rate out: x/100 Volume: 100...

dy/dx = (2/pi^(1/2))e^(-(x^2)) eq 1.17 My book makes a statement about the symmetry of the family of solutions to this diff eq I don't quite understand. "Symmetry. If we replace x with -x on both sides of 1.17, the right hand side is unchanged but the left hand side changes signs. So...

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.

Homework Statement The rate of change of the population p is proportional to the existing population at any time t: dp/dt = k_g*p where k_g is the growth rate. The world population in millions from 1950 through 2000 was 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2555...

(URGENT) Power series solution for ODE Homework Statement Supose there is an infinite series solution\sum b_{n}x^{n} for u''+4(x-(1/4))^2*u+C(x) = 0 where C(x) is a function (I get it in another problem, I'll put it in the relevant equations area), determinate the coefitients b_{0} b_{1}...

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...

Homework Statement (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 involving w and v Report your computed solution (wh(1),vh(1)) for h=1/10. Homework Equations The...

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 =...

y1 and y2 are solutions to the ODE L[y]=0=y''+p(x)y'+q(x)yWhat can you conclude about p(x), q(x) and the solutions on the interval I if i) W(x) = 0 for all X on I ii) W(x) = c for all X on I, c =/= 0 --- W(x) = y_1'y_2-y_1y_2' = C*e^{\int{p(x)}} i) W=0 so y1'y2=y1y2' And y1 and y2 are...

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 My computer is having major issues with latex right now, so sorry for not putting it in latex format. y'' + y' + (5/4)y = g(t) y(0) = 0, y'(0) = 0, g(t) = piecewise function {sint, o <= t < pi; 0, t>= pi Homework Equations Laplace transform The Attempt at a Solution I...

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.