Ode Definition and 1000 Threads

[b]1. Check that y(t)=1/λ ∫_0-t_〖f(s) *sin(λ(t-s) )ds〗 is the solution of the following initial value problem y''(t)+λ^2y(t)=f(t), λ>0, y(0)=0,y'(0)=0 Homework Equations [b]3. I tried to do integration by parts on y(t), but...

i am having issues solving an ODE it is given as y'= (1-2y-4x)/(1+y+2x) I've been told to find the particular solution when y(0)=1 please help

I had made a post in the past about the same problem and unfortunately I wasn't clear enough so I am trying again. I am studying an article and there I found without any proof that the solution of: Let ##g \in \mathbb{C}## and let ##u:(0,\infty)\to \mathbb{C}## $$ -u''+\lambda^2u=f\,\, on...

I am trying to solve an ODE and PDE and I am having problems coming up with a method for doing so. The PDE is: k1*(dC/dt) = k2*(dC/dx) But I have an ODE that is an expression for dC/dt: dC/dt = k3*C Where k1,k2 and k3 are constants. I planned to use the method of lines to get...

I am doing a little research project into numerical methods of solving ODEs where I do 1 half of learning about the basics of numerical methods and then look at a particular method (Linear multistep) and then the second half is looking at a particular example, applying what I've learned and...

-u''(z)+α2u(z)=f(z), u(0)=g(z), u(z)=0 as z→∞ -u''(z)+α2u'(z)=f(z), u(0)=g(z), u(z)=0 as z→∞ I am interested to solve these two boundary problems using Green's functions. It is noticed that z is complex variable. Can someone help me to do this?

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

Hi, everyone! This is my first post here, I need an hand with this equation! Homework Statement Solve the initial value problem: \begin{equation} \begin{cases} u''(x)+4u(x)=\cos(2x) \\u(0)=u'(0)=1 \end{cases} \end{equation} The Attempt at a Solution I started by solving the...

If one has a simple variable coefficient process like y'(t) = r(t)*y(t), is there a way to control it to a set point by feedback hitting the variable coefficients in r(t)? I am interested in feedback control of population processes. y'(t) = r*y(t) is simple proportional growth with a...

Homework Statement problem: Find a 1-parameter family of solutions of each of the following equa- tions. Assume in each case that the coefficient of dy \neq 0. (x + \sqrt{ y^2 - xy}) \mathop{dy} - y \mathop{dx} = 0 answer: y = ce^{-2\sqrt{1 - x/y}}, \;\;\; y >0, \, x< y; \;\;\; y =...

Hey I have taken a programming course. And I have learned about Simpson, Trapezoidal and the midpoint rule etc, I have programmed these. I have also implemented forward Euler, backward euler, Runge Kutta etc for solving ODE. I am wondering if there is any way to unify these two things, are...

Homework Statement Consider the following second order ODE $$ y'' + 2y' - y = e^{-x}, \quad y(0) = y'(0) = 1. $$ Convert this to a system of first order equations and use the pc33assisys MATLAB file to compute the solution for y(2). Homework Equations The Attempt at a Solution...

I am trying to solve this ODE and am stuck on this step! It is a mass balance of a tank where the volume and concentration are changing by time Fin*Co - Fout*C1 = d(C1*V)/dt Fin*Co - Fout*C1 = d(C1)/dt * V + d(V)/dt * C1 where V = A*h (area and height, where area is constant and height...

Here is the question: Here is a link to the question: Homogenous Differential Help with equation? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Note: I think there is a typo here but I'm not sure. Is there supposed to be a comma between the delta t/2 and y_n on K2 and K3, and delta t and y_n on K4? Homework Equations See above.The Attempt at a Solution Substituting dy/t = z gives \frac{dz}{dt} = 3z - 2ty - cos(t)...

Hi! I'm having a lot of trouble solving the following ODE: dx/dt = A - B*sin(x) where A and B are constants. My ODE skills are a bit rusty, and I wasn't able to find anything on the Internet that could help me, so could someone please show me how to solve for x in terms of t? I've...

This is my first time posting in this forum, I am not very familiar with the rules. I am a year 1 physics student, and I had only taken 1 variable calculus( I also know some basic linear algebra, e.g. how to calculate eigenvector in 2x2 situation, don't know Gram–Schmidt process for...

Hello, I'm currently modeling the profile of a droplet (sessile drop, axisymmetric) in matlab. I've coded differential equations, applied the solver, and I get a reasonable result, except that it spirals continuously. The ODE's in question are: \frac{dx}{ds}=cos(\theta)...

Here is the question: Here is a link to the question: General solution of dy/dt=k((y)(b-y))? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hi, y'' = y^2/x y(x) = ? Trial and error: y(x) = 2/x. I am glad to get a particular solution too. Thanks, kamke

This is really more of a mathematical question than physics. Given a RLC circuit, I will arrive at the following DE: \ddot{Q}+\frac{R}{L}\dot{Q}+\frac{1}{LC}Q-\frac{\epsilon}{L}=0 How do I solve for Q(t)??

Hi guys, Here is an equation that I have tried for few days to solve and still haven't succeeded, I'm interested to solve this 4th order wave equation to find u(x). ∫∫(A u(x) + B u(x)2 + C u(x)3 +D u''(x)) dx dx=0 the 4th term is second derivative of displacement u(x). I assume...

Here is the question: Here is a link to the question: Initial value problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement A mass of 40 g stretches a spring 10 cm. A damping device imparts a resistance to motion numerically equal to 560 (measured in dynes/(cm/s)) times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward...

Homework Statement A force of 2 lb stretches a spring 1 ft. A 3.2 lb weight is attached to the spring and the system is then immersed in a medium that imparts a damping force numerically equal to 0.4 times the instantaneous velocity. Find the equation of motion if the weight is released from...

Homework Statement Consider the general linear homogeneous second order equation: P(x)y'' + Q(x)y' + R(x)y = 0 (1) We seek an integrating factor μ(x) such that, upon multiplying Eq. (1) by μ(x), we can write the resulting equation in the form [μ(x)P(x)y']' + μ(x)R(x)y = 0...

Hello, everyone. I am currently a junior [physical] chemistry major and am picking out my future upper division electives. I've narrowed them down to a handful of classes and what I'm looking for is just a little background information on them, which ones might be better than others, general...

I am given the following ODE, and the instructions are to show whether it is exact or not, and then solve: $$(x+y)dy=(y-x)dx$$ My first step, is to put the equation in the form $$M(x,y)\,dx+N(x,y)\,dy=0$$: $$(x-y)dx+(x+y)dy=0$$ Next, I compute the partials: $$\frac{\delta M}{\delta...

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? $$ L\ddot{\theta} + \dot{x}\dot{\theta} + \ddot{x}\theta = 0 $$

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...

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...