Ode Definition and 1000 Threads

Homework Statement u'' + w20*u = cos(wt) w refers to omega. Homework EquationsThe Attempt at a Solution I'm not sure where to begin on this. For starters, it's a multiple choice problem, and all the answers are given in terms of y, so I'm not sure if u is supposed to replace y' or something...

Homework Statement Solve: \frac{d^{2}y}{dx^{2}} + \omega^{2}y = 0 Show that the general solution can be written in the form: y(x) = A\sin(\omega x + \alpha) Where A and alpha are arbitrary constants Homework EquationsThe Attempt at a Solution I know that I will need to change variables for...

Homework Statement y'' + 4y = t2 + 6et; y(0) = 0; y'(0) = 5 Homework Equations The Attempt at a Solution So, getting the general solution, we have r2 + 4 = 0, so r = +/- 2i So the general solution is yc = sin(2t) + cos(2t) I then used the method of undetermined coefficients to figure that...

Homework Statement Find the fundamental solution to ty''' - y'' = 0 Homework EquationsThe Attempt at a Solution I think I'm missing something really obvious, but I have the characteristic polynomial: t\lambda^3 - \lambda^2 = 0 Solving the equation: \lambda^2 (t\lambda - 1) = 0 I get zero...

Solve the DE using an appropriate substitution. (x-y)dx+xdy=0 First step is to determine the substitution. I was told for homogeneous ODEs to always make the substitution y=ux but the substitution u=x-y looks better. Let u = x-y then u'=-y' which means y'=-u' rewrite the original equation...

I have determined the solution to a nonlinear first order ordinary differential equation but am struggling to rearrange the result, I have that $$\\ln(R)+\frac{mR^{n-1}}{n-1}=\bar{w}_{\infty}\xi+C.$$ How would I rearrange this equation for $$R$$?

Homework Statement Solve the given differential equations with missing x. y'' + y = 0 Homework Equations y = c_1cos(x) + c_2sin(x) This is the answer given in the back of the book. However, I can't sem to get my answer to agree The Attempt at a Solution First, I made some substitutions: y'...

Homework Statement I need to (analytically) solve a system of coupled second-order ODEs: (A) \frac{du}{dt} - fv = \Omega^2x (B) \frac{dv}{dt} + fu = \Omega^2y where u = \frac{dx}{dt} v = \frac{dy}{dt} subject to the initial conditions u(t=0) = U and v(t=0) = 0. Homework Equations --- The...

Homework Statement This is not the exact problem that I want to solve but I will use this as a guidance tool: ##y'' - (y')^2 + y^3 = 0## where y is the function of x 2. The attempt at a solution I tried doing a substitution ##u(x) = y'(x)## which leads to ##u' - u^2 + y^3 = 0## where both u...

Homework Statement So this is part of a broader problem about the quantum harmonic oscillator, but there's one particular bit of mathematics I'm stuck on. We have the differential equation: y''(x) +(ε-x2) y = 0 And I'm told that we're to examine how y behaves as x tends towards...

Homework Statement the first one y'=\frac{y^{2}+xy^{2}}{x^{2}y-x^{2}} the second one xyy'=\frac{x^{2}+1}{y+1} Homework Equations The Attempt at a Solution i separated x and y variable then integrate both of them in the first one ∫\frac{y-1}{y^{2}}dy=∫\frac{1+x}{x^{2}}dx...

I'm going to need a little help with this one. I get an answer but it doesn't make sense. The question states According to Newton's law of cooling, the time rate of change of temperature T(t) of a body immersed in a medium of constant temperature A is proportional to the difference A-T. That...

Homework Statement Solve the 2nd order nonlinear differential equation, with initial conditions y(0)=0 and y'(0)=1 y''=2ay^3-(a+1)y with a within [0,1] It would be greatly appreciated if someone could point me in the right direction on this. Thanks! Homework Equations The Attempt at a...

I'm having a lot of trouble with this problem. I'm also having a lot of trouble inputting it into LaTeX. I hope you can follow even though the markup isn't good. I'm trying to find a formula for the general solution of $ax^2y''+bxy'+cy=0$ where $y=x^r\ln(x)$ when $(b-a)^2-4ac=0$; using...

Hi How do you calculate the following indefinite integral: \int \frac{2x}{125+3t} dt a step by step solution would be appreciated

This is not homework but is part of the solution process of an ODE and I cannot understand how the author made a derivation step. After a change of variable in the original ODE, the ODE in the new independent variable has a standard method of solution. But instead of using this method, the...

I am learning how to solve 1st order linear ODEs using the integrating factor.However, I run into confusion at the definition of a linear ODE. According to a reliable source, a linear ODE must have the form: (dy/dt) + p(t)y= g(t) I don't understand what it means for an ODE to be...

Homework Statement x \frac{du}{dx} \ = \ (u-x)^3 + u solve for u(x) and use u(1) \ = \ 10 to solve for u without a constant. Homework Equations The given hint is to let v=u-x The Attempt at a Solution This equation is not separable and the book wants me to make it separable...

For this problem, I am stuck on the actual system. I don't see what substitution I can make, and the fact that ##u(v)## is a piece-wise function is tripping me up. How the heck do I approach this?? This doesn't look like a standard problem at all.

i just signed up here so i hope this is the right place. i need to solve a set of 2 non-linear ordinary differencial equations. i tryed using NDSolve but it doesn't really work so I am not sure what's wrong with my code. here is my code (copy paste): c = 0.1; Subscript[sys, B]...

Homework Statement Solve the below differential equation Homework Equations The Attempt at a Solution I have attached my attempt at solution. But I don't how to get rid of (ln y) term in my equation i.e, i Don't know how to write in terms of y. Please help

For a regular LR circuit (L and R in series) and with a AC voltage: I tried to derive the solution myself. https://www.dropbox.com/s/jmsu9j0vt91ze8x/LRcircuit.jpg So first I solved with undetermined coefficients, plugged them in, and then solved with Cramer's Rule. Then I added...

The equation for this physical model is: http://upload.wikimedia.org/wikipedia/commons/f/fb/RLC_series_circuit_v1.svg And for this is: http://upload.wikimedia.org/wikipedia/commons/d/d0/RLC_parallel_circuit_v1.svg But and if now I add a source of current in those schemes, the...

Hello everybody. Solving a problem in Physics I run into a system of equations that I do not know how to solve, I would appreciate some help. Here is the system: \ddot{x}+4\dot{x}^2=C_1e^{y} \dot{y}^2=C_2\ddot{x} The dependent variables are x,y. C_1 and C_2 are some constants. I try...

Given the following ODE: ##ay''(t) + by'(t) + cy(t) = 0## The following solution: ##y(t) = c_1 \exp(x_1 t) + c_2 \exp(x_2 t)## is more general than: ##y(t) = A \exp(\sigma t) \cos(\omega t - \varphi)## ? Why?

1. The problem is to find the series solution to the following differential equation $$ x^2 \frac{d^2 x}{dx^2}+x\frac{dy}{dx}+(x^2 - 1)y $$ 3. Using the ansatz $$ y = \sum _{\lambda = 0}^{\infty}a_{\lambda}x^{k+\lambda}$$ the solution to the indicial equation was found to be...

Hi everyone. I have a copy of Ordinary Differential Equations by Vladimir Arnold. I'm hoping to learn more about differential equations, building up to differential equations on manifolds. I've heard that this is a great book, but I've also heard Arnold sometimes leaves out important details...

Homework Statement $$y'' + \frac{1}{x}y' - \lambda y = 0$$ where ##x \to \infty \implies y \to 0## and ##x \to 0 \implies y' \to 0##The Attempt at a Solution to begin, this was initially a pde, and I've applied separation of variables. to solve this ODE, it seems i cannot assume ##y=e^{rx}##...

If a 2nd order linear ODE: can written in terms of natural frequency ω0 and damping ratio ζ: being: So, it too can be written in terms of exponential decay/growth σ and angular frequency ω?

Hi, I'm solving a problem numerically that takes the form Q_{ij} \ddot{y}_j +S_{ijk}\dot{y}_j\dot{y}_k +V_i=0, where (Q_{ij},S_{ijk},V_i) are all functions of the dependent variables y_i. The dependent variables are all functions of the variable t. The resolution of this spectral...

Homework Statement 1) Find the general solution of y''+ω02=Ccos3(ωx) 2) Show there exists two frequencies at which resonance occurs and determine them The Attempt at a Solution I've tried the method of undetermined coefficients, assuming a solution of the form y=(Acos(ωx)+Bsin(ωx))3...

I'm trying to analyze the following Ito stochastic differential equation: $$dX_t = \|X_t\|dW_t$$ where X_t, dX_t, W_t, dW_t \in \mathbb{R}^n. Here, dW_t is the standard Wiener process and \|\bullet\| is the L^2 norm. I'm not sure if this has an analytical solution, but I am hoping to at...

Hello I am trying to solve this ODE dx/dt=(f(x)+g(t))^(1/2) I have been recalling what I learn in my ODE course and looking at my old textbook but I did not find what method is appropiate to try...any suggestions? Thank you very much!

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

I'm confused by problem 2.31 in mathematical tools for physics. Problem: 2.31 The Doppler effect for sound with a moving source and for a moving observer have different formulas. The Doppler effect for light, including relativistic effects is different still. Show that for low speeds they are...

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

Which the difference between diff equations of kind: \frac{dy}{dx} = \exp(x) \frac{dy}{dx} = 1/x and diff equations of kind: \frac{dy}{dx} = y \frac{dy}{dx} = \frac{1}{\exp(y)} ?

Given a implicit ODE like F(x, y(x), y'(x), y''(x)) = 0, why your explicit form is y''(x) = f(x, y(x), y'(x))? Why a ODE is explicited always with y of higher grade?

If we have a constant coefficient second order homogeneous ODE, the way to solve this is to suppose a solution of the exponential type. This yields a second order polynomial equation (the "characteristic equation") that the exponent must satisfy. In case the solutions of the characteristic...

I want to solve y''+y'+y=(sin(x))^2 and try to use y=Ae^{ix} but then when I square it I get A^2 e^{2ix} I found y' and y'' and solved for A and it didn't work I guess I could use the formula for reducing powers but I would like to try and get around that.

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

Homework Statement I wondered if anyone could advise me how to proceed with this question. The solution to the differential equation \frac{dQ}{dt}= \frac{1}{2}+\frac{1}{4}sin(t)-\frac{Q}{50} is Q=25+(\frac{sin(t)-625cos(t)+63150e^{-\frac{t}{50}}}{2501}) when Q_0= 50 "The long-term...

Homework Statement I have been trying to follow a solution to a problem I had but do not quite understand the whole thing. I wondered if anybody could clear it up for me. Let a_0 be the initial value of 'a' for which the transition from one type of behaviour to another occurs. The...

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

Homework Statement Can anyone point out where I have gone wrong with this? Verify that the given function is a solution of the differential equation. y' -2ty =1 y= e^{t^2}\int^t_0 e^{-s^2}ds+e^{t^2} The Attempt at a Solution The steps I have taken are the following: i)...

Homework Statement In my ODE class, we learned how to solve first order ordinary differential equations which are not exact yet but exact after multiplying by the right integrating factor. The integrating factor we learned about take one of the five forms: f(x), f(y), f(xy), f(x/y), and...

Hello. I have a set of ODE where 1) \frac{dv_x}{dt}=\frac{q(t)B}{m}v_y 2) \frac{dv_y}{dt}=\frac{q(t)B}{m}v_x 3) \frac{dv_z}{dt}=0 Following the strategy to solve a simple harmonic oscillator, I differentiate (1) to get 4) \frac{d^2v_x}{dt^2}=\frac{q(t)B}{m}\frac{dv_y}{dt}+q'(t)v_y...

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

I'm trying to solve this ODE R'(t)=\frac{-a}{R(t)^2} numerically in Mathematica (a, b are non-zero constants). Here's what I have: NDSolve[{R'[t]==-a/R[t]^2, R[0]==b, WhenEvent[R[t]==0, end=t; "StopIntegration"]}, R, {t,0,1}] It's returning with NDSolve:::ndnum : Encountered...

Hello guys, I would like to ask some questions regarding my coursework, which is about 2nd ODE and multivariable calculus. Since we have the one-dimensional wave equation and values for the string stretched between x=0 and L=2: 0≤x≤L, t≥0 The string is fixed at both ends so we have ...