Ode Definition and 1000 Threads

Homework Statement The first task was to solve ##(1-x)y''+y=0## about x = 0, which I've already found. Now I have to use this solution to solve ##\color{red}{xy''+y=0}## about x = 1. Homework Equations The Attempt at a Solution I found the solution about x = 0 (after a lot of...

Hey, guys Can you please help me to spot mistakes in numerical solution of following diffusivty equation: ∂P/∂t= 0.001127*k/(μ*ϕ*c_t )*((∂P/∂x)^2*c+(∂^2 P)/(∂x^2 )). Matlab give the following command: Undefined function or variable 'r'. Error in function_handle2 (line 9) for...

Homework Statement Solve ##(1-x)y''+y=0## at the point ##x_0=0##. Use this solution to find a solution to ##xy''+y=0## around the point ##x_0=1##. Homework Equations The Attempt at a Solution ##(1-x)y''+y=0## ##(x-1)y''=y## ##\displaystyle\sum_{k=2}^\infty a_k k...

Homework Statement Solve for y' = x^2y The Attempt at a Solution There's something that's been really bothering me about this question and similar ones. We assume that the solution to the ODE will take the form y = \sum_{n=0}{a_nx^n} After finding y', plugging in the expressions...

Homework Statement ODE: y'' + 4y' + 3y = f(t) f(t) = (?? HELP - What's the mathematical term to describe these? I can't seem t o find it in my notes :cry: ) 1, 0 ≤ t < 2 t², 2 ≤ t < 3 0, t ≥ 3 Write a brief description on how you would solve this ODE using Laplace transforms. Also use the...

Homework Statement I've got an IVP where, 3xy+y2+(x2+xy)y'=0, y(1)=0 The Attempt at a Solution I've solved to get, x2y(x+\frac{1}{2}y)=0 Is it correct to say, x=0 or y=0 or y=-2x, Since y= 0 is the only solution that fits y(1)=0, then y=0 \forallx

I've got this problem, with relation to rates. [A] is the concentration of one substance, is the concentration of another, etc. [R] is a general reactant, [P] is a general product, [S] is a general substance (which thus relates to both reactants and products). But you won't actually need...

If you look on the last page http://www.mathhelpboards.com/f49/orbital-mechanics-notes-3682/, you will see the some equations. I don't see how to go from the 2nd to last equation to the last equation.

$$ -\sum_{n = 0}^{\infty}n^2\omega^2C_ne^{in\omega t} + 2\beta\sum_{n = 0}^{\infty}in\omega C_ne^{in\omega t} + \omega_0^2\sum_{n = 0}^{\infty}C_ne^{in\omega t} = \sum_{n = 0}^{\infty}f_ne^{in\omega t} $$ How can I justify removing the summations and solving for $C_n$? $$...

I encountered the following second order nonlinear ODE while solving a problem in electrostatics. The ODE is: \frac{d^{2}V}{dx^{2}} = CV^{-1/2} How can I solve this? Regards. Homework Statement Homework Equations The Attempt at a Solution

I have no idea how to start solving this ODE: y''(x)+(μ^{2}*c(x)+k^{2})y=0 Where c(x)=A+Btanh(ρx) with constant A,B,ρ,μ,k Could anyone give me a nudge in the right direction? Cheers.

Is there a way to break this up into a system of ODEs? $$ L\ddot{\theta} + \dot{x}\dot{\theta} + \ddot{x}\theta = 0 $$

Hi, I am currently trying to plot and animate a wave function using the Schrodinger equation. I currently have the following finite difference equation:- i(\psi(x, t+\Delta t)-\psi(x,t))/(\Delta t)=-(1/2)*(\psi(x+\Delta x, t)+\psi(x-\delta x, t)-2*\psi(x,t))/((\Delta...

Homework Statement Use the method of reduction of order to find another independently linear solution y2(x) when given one solution. x^2y'' - x(x+2)y' + (x+2)y = 0 y_1(x) = x The Attempt at a Solution Hopefully y2(x) will take the form of v(x)y1(x) or I have no idea how to solve the ODE...

So, I was following the derivation in my physics book of: x(t) = c_1e^-(\frac{\gamma t}{2})\cos(\omega_d t)+c_2e^-(\frac{\gamma t}{2})\sin(\omega_d t) Until they simply get to this in one step: Ae^-(\frac{\gamma t}{2})\cos(\omega_d t + \phi) I've tried reading many other sources for this...

Homework Statement I have a population problem where: \frac{dy}{dt} = ay - by^{2}-\frac{c*y^{3}}{d+y^{3}} I need to find an expression for y(t). I'm not looking for the answer, just some advice/ helpful hints. Thank you. Homework Equations The Attempt at a Solution I...

I'm having issues approaching this problem. I need to solve for Homework Statement Given the following equation, I need to find the max change in x(t) as y(t) changes, given bounds y_{max} and y_{min}. \frac{dy}{dt} + a \sqrt(y(t)) = b x(t) Homework Equations All ODE methods, MATLAB, or...

How can I extract time data from a system 2nd order ODEs in Mathematica?

Can this be written as a system since it only has theta? $$ U' = -\frac{mgb}{\sin^2\theta} - \frac{Mgb\cos\theta}{\sin^2\theta} = \frac{gb}{\sin^2\theta}(m - M\cos\theta). $$

I thought today of the next DE: y''(x) = y(x)e^{y'(x)} Not sure if it has applications, obviosuly I tried to find a solution via power series around x=0. It seems tough to look for a general recurrence equation for the coefficients. Here's what I have done so far. y(x)=\sum_{n=0}^{\infty}...

I've become a little confused about why no one cares to actually explicitly solve the Matrix Ricatti Differential Equation (RDE) of the form: $$ -{\dot{P}} = Q + PA^T + A^TP + PBB^TP $$ where BB^T, Q, P are a positive-definite matrices, and A, BB^T, Q, P \in \mathbb{R}^{n \times n} This...

Inthis article, the authors present the inhomogeneous equation $$\ddot{\phi}_2 + \phi_2 + g_2\phi_1^2 + \omega_1\ddot{\phi}_1 = 0,\tag{11}$$ where $$ \phi_1 = p_1 \cos(\tau + \alpha), \tag{13}$$ The original solution of the inhomogeneous equation is: $$\phi_2 = p_2\cos(\tau +...

Homework Statement Obtain intervals x∈[0,α] for the existence of a unique solution dy/dx = f(x,y) = e^-(y-x)^2; y(0) = 0 on the rectangle B = [0,a]x[-b,b] Homework Equations The Attempt at a Solution Since both dy/dx and it's partial derivative of y are both continuous, a unique...

Homework Statement A 50kg mass is attached to a spring and hung from an overhead beam. The Force on the spring when extended 2 meters from rest is 50N. The resting length of the spring is 1m. 1) Obtain the ODE to solve for the velocity as a function of position (NOT time) 2) Solve the...

Hi all, I have a nonlinear ODE in the following form: a x'' + b |x'|x' + c x' + d x = y where x and y are functions of time and a,b,c and d are constants. As far as I can tell the only way to solve this is numerically, something I've managed to do successfully using a Rung-Kutta scheme...

Homework Statement Find a solution of the IVP \frac{dy}{dt} = t(1-y2)\frac{1}{2} and y(0)=0 (*) other than y(t) = 1. Does this violate the uniqueness part of the Existence/Uniqueness Theorem. Explain. Homework Equations Initial Value Problem \frac{dy}{dt}=f(t,y) y(t0)=y0 has a...

Homework Statement We have y'' + 4y' + 4y = 0 ; find the general solution. Homework Equations Reduction of Order. The Attempt at a Solution So when determining the roots of the characteristic equation, -2 was a double root, and therefore we can't simply have c1e-2t + c2e-2t. So I thought...

Homework Statement Suppose u, v are two linearly independent solutions to the differential equation u''+p(x)u'+q(x)v=0. If x0,x1 are consecutive zeros of u, then v has a zero on the open interval (x0,x1) Homework Equations The Attempt at a Solution I'm trying to use the...

Homework Statement Two reservoirs are connected. Water drains from one reservoir to the other, governed by the following ODE: dh/dt= -k1*(h)^0.5 -k2*(h-H)^0.5 , H<0, k1,k2>0 Does an equilibrium exist? What happens in terms of Picard's Existence Theorem? Draw a phase diagram of possible h*...

Homework Statement Find general solution to: xy''+2y'+4xy=0 Homework Equations Frobenius Method or Bessel's Equation The Attempt at a Solution I know how to get the roots for this problem (which are r1 = 0 & r2 = -1). But not I don't know what to do with these roots. I know that...

I am getting this error in Mathematica from the code below: Computed derivatives do not have dimensionality consistent with the initial conditions ClearAll["Global`*"] \[Mu] = 398600; s = NDSolve[{x1'[t] == x2[t], y1'[t] == y2[t], z1'[t] == z2[t], x2'[t] == -\[Mu]*x1[t]/(x1[t]^2 +...

Hi everyone, I have an inhomogeneous Bernoulli type ODE given by u'(t) = \kappa u(t) + \ell(t) u^{\gamma}(t) + v(t),\ \ \ u(T)=b>0,...(1) where t\in[0,T],\ \ \gamma\in (0,1) . My concern is that how to prove the existence and uniqueness of the solution u(t) for all t\in [0,T]...

Homework Statement First time I've had to deal with ODEs, an I'm pretty confused. This SHOULD be a simple ODE for finding air resistance, that is only dealing with the y vector (up and down in this case) m\frac{dv_{y}}{dt}=mg-kv_{y} Homework Equations F=ma f=-kV The Attempt at a...

Here is the question: Here is a link to the original question: Solve this differential Equation: df/dy(t) + f(y) =sin(2y)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hi everyone, Im looking for an autonomous first order ode that has the following properties. For dependent variable x: x(t=∞)=0 x(t=-∞)=0 and the function x(t) has one maximum. Any help would be great. Rgds...

Homework Statement Identify the region that the DE will have a unique solution. y' = \frac{y^2}{x^2+y^2} The Attempt at a Solution \frac{\partial f}{\partial y} = \frac{2x^y}{(x^2+y^2)^2} I'm a bit rusty with my domains, but here is what I've got. x: (-∞, -2) U (2,-∞) y...

Homework Statement Hi, Wondering if anyone can give me some help with reducing this 3rd order ODE to a first order problem, so it can be written in the form u' = f(u, t) Homework Equations The 3rd order ODE is: x'''(t) + x''(t) + 2x'(t) + 2x(t) = 2t^2 + 4t - 5; The initial values...

Homework Statement (y^2 + xy)dx - x^2dy = 0 The Attempt at a Solution Put it into derivative form. y^2 + xy - x^2 \frac{dy}{dx} = 0 \frac{dy}{dx} - \frac{y^2}{x^2} - \frac{xy}{x^2} = 0 \frac{dy}{dx} + \frac{-1}{x}y = \frac{1}{x^2}y^2 I recognized this as a Bernoulli equation...

I would like to solve the non linear ODE \frac{d}{dx}f(x)=a f(x)+ b f^3 (x) with the boundary f(0)=0\quad f(+\infty)=f_0 How to find analitical solution?

Dear All, What type of packages exists out there to the solution of the ODE equations in engineering especially for the M*X''+C*X'+K*X = F ; 2nd order equation, where none of the variables denoted as M, C, K and F are function of the time and are mass, damping, stiffness and force matrices...

Given an open connected subset D of the (t,x) plane and a function f\in C(D,\mathbb{R}), we say \varphi\in C^1(\text{proj}_1D,\mathbb{R}) is a solution of the first order differential equation x'=f(t,x) if and only if \forall t\in \text{proj}_1D,\quad (t,\varphi(t))\in D and \forall t\in I...

Homework Statement basically solve \frac{d^{2}y}{dx^{2}} + 4\frac{dy}{dx} + 4y = cos2x Boundary conditions are y=0, dy/dx =1 at x=0 Homework Equations The Attempt at a Solution I am having trouble getting the coefficients to the solution. I got the complementary function as...

Question: Show that the system x'= x-y-x[x^2 + (3/2)y^2] y'= x+y -y[x^2 + (1/2)y^2] has at least one periodic orbit. I know that I need to apply Poincare-Bendixson Theorem. I can prove the first three points of it easily, but to create a trapping region, I believe that I need to...

Homework Statement I'm currently taking a course on ordinary differential equations. I am now reading through the lecture slides but I'm not really sure about the " factorising the equation " part onwards: Homework Equations The Attempt at a Solution I'm not sure what is...

Homework Statement Dear all, please help. I have tried this question and came up with strange numbers, my fortran is definitely not correct. Please help! When the effect of the air resistance is taken into account, the equation of motion for a particle of mass m falling vertically in a...

Hi. If I have a homogeneous ODE with constant coefficient system in the form of 2x2 matrix: X'=A X, A is a 2x2 matrix. How do I solve this using wolfram or matlab?

Homework Statement Solve the following systems by either substitution or elimination: dx/dt = y dy/dt = -x + cos(2t) Homework Equations I know the solution is: x(t) = c_1cos(t) + c_2sin(t) - 1/3cos(2t) y(t) = -c_1sin(t) + c_2cos(t) + 2/3sin(2t) The Attempt at a Solution x' = [ 0 1; -1...

Homework Statement \dot{ω_{1}} = λω_{2} +μ \dot{ω_{2}} = -λω_{1} Homework Equations λ and μ are real, positive constants ω_{1}(0) ≠ 0 ω_{2}(0) ≠ 0 The Attempt at a Solution I know that the general solution will be in the form ω1(t) = A sin ωt + B cos ωt + C ω2(t) = D sin...

Homework Statement I'm trying to understand the simplification of the general solution for homogeneous linear ODE with complex roots. Homework Equations In my notes, i have the homogeneous solution given as: y_h (t)= C_1 e^{(-1+i)t}+C_2e^{(-1-i)t} And the simplified solution is given as: y_h...

The ODE to solve via variation of parameters is ##(1-x)y''+xy'-y=(1-x)^2##. Knowing that ##e^x## and ##x## are solutions to the homogeneous ODE. Now if I call ##y_1=x## and ##y_2=e^x##, the Wronskian is ##W(y_1,y_2)=e^{x}(x-1)##. According to...