Ode Definition and 1000 Threads

Find the eigenvalues λ, and eigenfunctions u(x), associated with the following homogeneous ODE problem: {u}''\left ( x \right )+2{u}'\left ( x \right )+\lambda u\left ( x \right )=0\; ,\; \; u\left ( 0 \right )=u\left ( 1 \right )=0 Solution: Try u\left ( x \right )=Ae^{rx} , which gives...

Homework Statement Solve the following system for 0<t<5 u^\prime = u-e^{-2t} v, u(0) = 1 v^\prime = u+3v, v(0) = -2 using Forward Euler method and implement the numerical scheme into a MATLAB code. Homework Equations Forward Euler : \vec x^(\prime)_{n+1} = \vec F(t,\vec x)...

This is a request about the second order differential equation y'' + (k^2 + f(r))y(r) = 0 (1) where k is a (real) constant and f(r) is a real valued function of r that has some constraints regarding integratability. According to...

Hi,The problem I am trying to solve is in a section on first order ODEs. It is problem 25 in section 2.1 of Boyce & DiPrima's Elementary Diff Eq (5th Ed). The problem serves as an introduction to the variation of parameters, but again, it is in the first section of the book that introduces first...

Homework Statement Hi, I was wondering if someone could help me create a basic differential equation in Simulink. I'm trying to create the following equations http://imageshack.com/a/img197/1379/cic.PNG I tried using this as an example...

I'm trying to solve this equation analytically, but I can't even find the auxiliary equation or general solution! Km = 0.5 C*e = 0 K2 = 0.03 K1 = 0.05 x* = 49

Hi, Homework Statement I have the following ODE: y′′−2xy′+2αy=0 I'd like to determine the first three eigenfunctions. Homework Equations The Attempt at a Solution The solution y(x) may be recursively represented as: an+2=an(2n−2α)/[(n+2)(n+1)] I have found the eigenvalues to be...

I'm trying to find a general solution for the logistic ODE \frac{dU}{dx}=A(I-U)U, where A and U are square matrices and x is a scalar parameter. Inspired by the scalar equivalent I guessed that U=(I+e^{-Ax})^{-1} is a valid solution; however, U=(I+e^{-Ax+B})^{-1} is not when U and A don't...

I managed to stumble upon a differential equation such as the one above while doing some torque calculations and am wondering if and how to find the solution to it. I'm not that well versed in differential equations, so any help would be appreciated. Edit: A method to graph an integral line for...

how do we solve an ODE which has forcing function in terms of Fourier series? i have attached a pdf file of the problem.

Here is the question: I have posted a link there to this thread so the OP can view my work.

Here is the question: I have posted a link there to this thread so the OP may see my work.

By using frobenius method I find the roots of the indicial equation of a 4th order ODE to be 0, 1, 1, 2 Now, what is the form of the corresponding series solution of this equation with log terms?

Homework Statement Solve the initial value problem: x^{2}{y}'' + x{y}' + y = 0, x>0, y(1)=1, {y}'=2 Homework Equations y=x^m The Attempt at a Solution x^{2}(m(m-1)x^{m-2})+xmx^{m-1} + x^{m} x^{2}(m(m-1)x^{m-2})+xmx^{m-1} + x^{m} x^{m}(m(m-1) + m + 1)...

Consider \frac{d^{2}y}{dx^{2}}+\frac{k}{x^{2}}y = 0. Show that every nontrivial solution has an infinite number of positive zeroes if k > 1/4 and a finite number if k ≤ 1/4. Solving gives: y = Asin(\sqrt{k}ln(x)) + Bcos(\sqrt{k}ln(x)) And setting y = 0 gives: tan(\sqrt{k}ln(x)) =...

Dear all, I have problem to find the differential equation for my circuit shown in the attached picture. For input I have a current source, and the output is the voltage U (the voltage between the first and the ground node). I need the ODE to find the mathematical response of the system...

Here is the question: I have posted a link there to this thread so the OP can see my work.

Homework Statement A dynamical system has a response, y(t), to a driving force, f(t), that satisfies a differential equation involving a third time derivative: \frac{d^{3}y}{dt^{3}} = f(t) Obtain the solution to the homogeneous equation, and use this to derive the causal Green's function...

Fint the exact solution of the system dy/dt = -15y-25z dz/dt=-47y-85z with inital condition y(0)=2, z(0)=5 either by writing the equation in matrix form as dx/dt =AX where x=(y z) and diagonalising the matrix A, or otherwise. Using fortran programming with second order adam bashforth...

Adapt the fortran programming using second order adams bashforth method to generate a numerical solution of the Lorenz system: dx/dt =-10x+10y dy/dy=28x-y-x*z dz/dt= x*y- (8/3)*z with initial condition x(0)=y(0)=0, z(0)=2 slightly perturbed. Plot x and z against t runs from 0 to 15, and also z...

In Bessel's ODE x^{2}y''+xy''+(x^{2}-\nu^{2})y=0, why must \nu not be less than zero? I have looked it up, but I do not find a satisfying answer anywhere.

Hello, I am working on a research problem and I am not sure whether or not I will be able to figure this out in a suitable amount of time. I have never solved a single elliptic integral and they do seem non-trivial to gain an understanding of (most of the books I've glanced at assume a very...

Homework Statement y''+6y=f(t), y(0)=0, y'(0)=-2 f(t)= t for 0≤t<1 and 0 for t≥1 Homework Equations The Attempt at a Solution L{y''}+6L{y}=L{t}-L{tμ(t-1)} where μ(t-1) is Unit Step Y(s)=L{y} sY(s)-y(0)=L{y'} and y(0)=0 s2Y(s)-sy(0)-y'(0)+6Y(s) where y(0)=0 and...

Homework Statement Let y(x)=\sumckxk (k=0 to ∞) be a power series solution of (x2-1)y''+x3y'+y=2x, y(0)=1, y'(0)=0 Note that x=0 is an ordinary point. Homework Equations y(x)=\sumckxk (k=0 to ∞) y'(x)=\sum(kckxk-1) (k=1 to ∞) y''(x)=\sum(k(k-1))ckxk-2 (k=2 to ∞) The Attempt at a Solution...

Homework Statement I am looking to solve the r(λ) null Schwarzschild geodesic in terms of the affine parameter λ, but I have not seen this done anywhere and I am not sure that it is even possible to do this somewhat close to analytically. As best I know there is no use-able boundary...

Homework Statement . Find all the solutions of the equation: ##\dfrac{\sin(y)}{x}dx+(\dfrac{y}{x}\cos(y)-\dfrac{\sin(y)}{y})dy=0## knowing that the equation admits an integrating factor ##u## of the form ##u(x,y)=h(\dfrac{x}{y})## The attempt at a solution. If I call...

Homework Statement I am trying to find the recursion relation for the coefficients of the series around x=0 for the ODE: y'''+x^2y'+xy=0 The Attempt at a Solution Therefore letting: y=\sum_{m=0}^\infty y_mx^m \therefore y'=\sum_{m=1}^\infty my_mx^{m-1} \therefore...

Homework Statement Let y(x)=\sumckxk (k=0 to ∞) be a power series solution of (x2-1)y''+x3y'+y=2x, y(0)=1, y'(0)=0 Note that x=0 is an ordinary point. Homework Equations y(x)=\sumckxk (k=0 to ∞) y'(x)=\sum(kckxk-1) (k=1 to ∞) y''(x)=\sum(k(k-1))ckxk-2 (k=2 to ∞) The Attempt at a Solution...

Homework Statement Find the general solution of 2y' + y - (2y')*ln(y') = 0 Homework Equations The Attempt at a Solution I have no idea how to deal with this i mean none of the first order techniques work and it's mainly because I don't know how to deal with the ln(y'). I tried seperating...

Homework Statement Hello, We are getting a quick taste of Boundary Value Problems in my ODE class and the application is deflection of beams. Basically I get to the point where I need to solve for the constants, but each constant appears in each equation but the powers of L are throwing me...

The vector field F=<y,x> looks exactly like the the direction field for the system dY/dt = {dx/dt = y} {dy/dt = x} A few questions on this: Are the direction field of a system of ODE's the same as a vector field of calculus? In vector calc we take the line integral of a vector field...

I'm trying to decide between taking an ODE class or a PDE class next. I have already done Calculus 1,2,3 so I already know some ODEs and PDEs and linear algebra. I'm a 3rd year mathematics major with a minor in Statistics and I'm interested in applied mathematics.ODE course coverage: Ordinary...

Hello there, I hope I'm posting in the right section. I have been doing some work on evolutionary game theory and poker. I will give a brief description of how I got here. I have eight strategies i = 1, 2, \ldots, 8 and the eight proportions of the population playing each strategy is...

\[y'sin(x)= yln(y)\] Hi, I am trying to solve this one but i can't find the same result of the book: Here is my solution:

I haven't done ODEs in a while nor have a book handing. How do I tackle an equation of the form \[ 2xyy'=-x^2-y^2 \] I tried polar but that didn't seem to work.

Homework Statement $$ \left(\frac{du}{dx}\right)^2 = au^2 + bu + c $$ Homework Equations The Attempt at a Solution What method is used to solve and ODE of this form

Here is the question: I have posted a link there to this topic so the OP can see my work.

\sqrt{1-y^2}dx - \sqrt{1-x^2}dy=0, y(0)=\frac{\sqrt{3}}{2} rewriting the equation gives \frac{1}{\sqrt{1-x^2}}dx = \frac{1}{\sqrt{1-y^2}}dy Isn't this the integral for \sin^{-1}(x) & \sin^{-1}(y)? The back of book has y=1/2x+\frac{\sqrt{3}}{2}\sqrt{1-x^2}

Find the solution of the given initial value problem, and plot its graph. How does the solution behave as \(t\rightarrow\infty\) \(y^{(4)}-4y'''+4y''=0\) My work, which coincidentally I believe is incorrect... From the above differential equation, \(r^4-4r^3+4r^2=0\) \(r^2(r-2)^2=0\)...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement y''+3y'+3.25=3cost-1.5sintHomework Equations yh = e(a/2)t(Acost+Bsint) yp = Kcos(ωt)+Msin(ωt) [when r(x)=kcos(ωt) or ksin(ωt)]The Attempt at a Solution I got the homogeneous solution, which is e-1.5t(Acost+Bsint) but I am having trouble with the particular solution. I...

1. A spherical buoy of radius r floats half-submerged in water. If it is depressed slightly, a restoring force equal to the weight of the displaced water presses it upward; and if it is then released, it will bob up and down. Find the period of oscillation if the friction of the water is...

I have a physics problem right now, and I am so close to finishing it... The problem is to consider an undamped (no friction) forced mass-spring system. The forcing is given by $$F(t)=F_o\cos{\omega_ft}$$ The general ODE for this would be $$\ddot{x}+(0)\dot{x}+\omega_o^2x=f_o\cos{\omega_ft}$$...

Homework Statement Using method of frobenius about x=0 to solve: (1-x) y''+xy'-\frac{\alpha^2}{x^2}+=0 Homework Equations N/A The Attempt at a Solution 1. plug in series into the equation. 2. adjust the index off all the terms. 3. write the extra terms separately so that we have...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement Given \frac{dx}{dt} = -1.3x x_{1}(t)=e^{-1.3t} x_{2}(t)=4e^{-1.3t} Compute a solution for x(t) if x(0)=3 Homework Equations Superposition Principle and some ODE related Anyhow I refer to this http://www.youtube.com/watch?v=_ECd0Jn7y68The Attempt at a Solution First...

Here is the question: I have posted a link there to this topic so the OP can see my work.

A particle of mass m is subject to a force F(v) = bv^2. The initial position is zero, and the initial speed is vi find x(t) so far m*dv/dx*v = -bv^2 m*dv/dx = -bv integral m/-bv*dv = integral dx m/-b*ln(v) + a = x + b What do I do with the constants? i thought i was suppose to put...

Should I just assume that any problems that involve integrating factor will always result in a perfect integral pair? That's probably not the right terminology but for instance if I have a differential equation which has had an integrating factor multiplied to both sides, then the left hand side...

Hi all, I have an ODE of the form \frac{d^{3}\psi}{d\xi^{3}}-A\left(\psi+\xi\frac{d\psi}{d\xi}\right)=0, where \psi=C_{1}U(\xi)+C_{2}V(\xi). Is there any transformation or inventive manipulation I can use here to obtain an ODE for \sigma=U(\xi)+V(\xi)? As this is the quantity I would...