Ode Definition and 1000 Threads

Can anyone give me a hand with this question? I honestly have no idea how to do it? I was thinking for d(A)/dt=-d(B)/dt= -k1(A)+k-1(B) because the 2 on both sides cancels out? But this was completely wrong... Any ideas? :)

Homework Statement An object of mass ##5##kg is released from rest ##1000##m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant ##b=50##N-sec/m, determine the...

Homework Statement Find the general solution: $$\frac{dy}{dx}=(x+y+3)^{2}$$ Homework Equations The Attempt at a Solution Methods I have learned: separation of variables, integrating factor for linear equations, exact equations, and substitution. I don't even know where to begin...

For an ODE of order 2 like: X'' + λ*X = 0, how do I find the non-trivial solution in Mathematica 8? It's giving me only the trivial solution. In: ComplexExpand [DSolve[{u''[x] + \[Lambda]^2 u[x] == 0, u[0] == 0, u[a] == 0}, u[x], x]] and the out: u[x]--> 0 which is the trivial soln...

Homework Statement $$\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +{ w }^{ 2 }x={ F }_{ 0 }sinwt\quad \quad \quad \quad x(0)=0\quad \quad x'(0)=0$$ Homework Equations The Attempt at a Solution $$\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +{ w }^{ 2 }x={ F }_{ 0 }sinwt\quad \quad \quad \quad...

Homework Statement Construct a first order linear differential equation whose solutions have the required behavior as t approaches infinity. Then solve your equation and confirm that the solutions do indeed have the specified property. All solutions are asymptotic to the line y = 2 - t as t...

Homework Statement $$\frac{dy}{dx}+y=\left\{\begin{matrix}1, \ 0\leq x< 1 \\ 0, \ x\ge1 \ \ \ \ \ \ \ \end{matrix}\right.$$ Homework Equations The Attempt at a Solution $$P(x)=1$$ Integrating factor ##=e^{x}## For ##f(x)=1##: $$\frac{d}{dx}[e^{x}y]=e^{x}$$ Integrating...

Problem: xy'+2y=3x Attempt: Divide by x... y'+\frac{2y}{x}=3 I think I find the integrating factor by doing: e^{\int \frac{2}{x}dx} Not sure if that's right but if it is then the solution to the integral is just 2x. Any help is appreciated

Homework Statement Solve the initial value problem: $$sin(x)y' + ycos(x) = xsin(x), y(2)= \pi/2$$ Homework Equations The Attempt at a Solution Recognizing it as a Linear First-Order Equation:$$\frac{dy}{dx}+y\frac{cosx}{sinx}=x$$ $$P(x)=\frac{cosx}{sinx}$$ Integrating...

$$w'+2w=0\\ \frac { dw }{ dx } =-2w\\ I(x)={ e }^{ 2x }\\ \frac { dw }{ dx } { e }^{ 2x }=-2w{ e }^{ 2x }\\ \int { \frac { dw }{ dx } { e }^{ 2x } } dx=\int { -2w{ e }^{ 2x } } dx$$ Not sure what to do next.

Homework Statement Solve: ##x\frac{dy}{dx}-4y=x^{6}e^{x}## Homework Equations ##x^{-4}\frac{dy}{dx}-4x^{-5}y=xe^{x}## is equal to ##\frac{d}{dx}[x^{-4}y]=xe^x## The Attempt at a Solution The second equation above simplifies to the third (according to my textbook) but I can't figure out...

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

I've been studying Walter A. Strauss' Partial Differential Equations, 2nd edition in an attempt to prepare for my upcoming class on Partial Differential Equations but this problem has me stumped. I feel like it should be fairly simple, but I just can't get it. 10. Solve ##u_{x} + u_{y} + u =...

Homework Statement Find the ODE of the following (1) du/dy = -u (2) d^2u/dxdy = -du/dx Homework Equations For question 1, the answer is u= A(x)e^(-y) while for question 2, the answer is u= e^(-y)(B(X) + c(Y)) The Attempt at a Solution I've already solved the question, but...

2nd Order ODE "Contradiction"? To solve a 2nd order ODE, we can follow the steps as shown below. (Image 2 is a continuation from Image 1, apologies for the size difference.) :rolleyes: The method to obtain the solution is straightforward. Let's say \frac{d^2y}{dx^2}=ky If k = -1, a...

Homework Statement A mass of 5kg stretches a spring 10cm. The mass is acted upon by an external force of 10sin(t/2) Newtons and moves in a medium that imparts a viscous force of 2N when the speed of the mass is 4cm/sec. If the mass is set in motion from its equilibrium position with an initial...

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

Hey everyone I am going to be a freshman this fall (in college). I am currently having a dilemma in choosing my math class. In high school I took classes all the way up to Honors Differential Equations (ODE). In June I went to the university and signed up for Ordinary Differential Equation...

I'm trying to approximate f'(r) for the following equation using matched asymptotic expansions -\frac{1}{2}\epsilon ff''=\left[\left(\epsilon+2r\right)f''\right]' where \epsilon \ll 1 and with the boundary conditions f(0)=f'(0)=0, \quad f'(\infty)=1 The inner expansion which satisfies...

Ahoy! I'm trying to approximate f'(r) for the following equation using matched asymptotic expansions -\frac{1}{2}\epsilon ff''=\left[\left(\epsilon+2r\right)f''\right]' where \epsilon \ll 1 and with the boundary conditions f(0)=f'(0)=0, \quad f'(\infty)=1 The inner expansion which...

[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...

Homework Statement Consider the differential equation x' = f(t,x) where f(t,x) is continuously differentiable in t and x. Suppose that f(t+T,x) = f(t,x) for all t Suppose there are constants p, q such that f(t,p) > 0, f(t,q) < 0 for all t. Prove that there is a periodic solution...

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.

Hello, guys I am struggling with attaining stability values for u in solving the diffusion equation. The stability of u depends on the value of r from : D=1000; r0=1000; std=1.0; tau=1.0; IP=2500; %initial pressure % % Radial grid and inhomogeneous term nr=51; dr=r0/(nr-1)...

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 y}=-1\ne1=\frac{\delta...