Ode Definition and 1000 Threads

y = y' (1+t^{4} +y^{8}+t^{2}y^{2}) y(0) = 0 I tried separating the variables, but it doesn't work. Thanks in advance.

I am new to differential equations, any help would be great. I have a ODE of the second order u''x = e^x over the domain [1, 1] where u'(0) = 0 is a Neumann boundary on the ODE. I am trying to approximate the solution using the finite differences method, I can do Dirichlet boundaries with...

Homework Statement A spring and dashpot system is to be designed for a 32lb weight so that the overall system is critically damped. (a) How must the damping constant γ and spring constant k be related? (b) Assume the system is to be designed so that the mass, when given an initial velocity of...

I'm trying to follow a proof for the solution of the diffusion equation in 0 < x < l with inhomogeneous boundary conditions. \frac{d u_n(t)}{dt} = k( -\lambda_n u_n(t) - \frac{2n\pi}{l}[ (-1)^n j(t) - h(t) ] ) u_n(0) = 0 Now I just plain don't understand what kind of an ODE I have here. If...

Homework Statement The solution for the differential equation on this page http://electron9.phys.utk.edu/phys135d/modules/m5/Friction.htm#Drag checks out, but I can't figure out how they found it. Both my solution and theirs check out. A couple people I asked for help reached the same...

Can anyone help with the following: dy/dx = ay / (bx2 +xy ) a,b constants thanks,

Homework Statement Find a basis of solutions. Homework Equations (1-x^2)y''+(1-x)y'-3y = 0 The Attempt at a Solution Using the series approach, having: y=\sum_{n=0}^{\infty}a_nx^n I ended up with an equation representing the coefficients for x^0 2a_2+a_1-3a_0 = 0 I'm...

If I produce two different sets of data with ode113, that are based on the exact same inputs, but one is longer than the other (i.e. tf is larger for one set, we'll call it A. Both A and B have the same ti). If I compare the two plots with imagesc(A) (so that the vertical axis represents the...

Homework Statement Find a value of the constant r such that both e^rt and te^rt are solutions to the ODE ay''+by'+cy=0 Homework Equations The Attempt at a Solution can anyone guide me with this question please. I am not sure where to start. I know that e^rt is always a solution...

found my mistake... thanks

Homework Statement Verify that the following ODE can be reduced to an ODE of separable variables. \frac{dy}{dx} =f(ax+by+c) where a, b and c are constants.2. The attempt at a solution I think I must show that there exist functions g and h such that g(y)dy=h(x)dx. I have that dy=f(ax+by+c) dx...

Homework Statement A stirred tank reactor that initially contains a volume V(0) = V_0 of water. Suppose that a stirred solution of salt at concentration S is pumped in at a rate of F_in = F litres/hr and the well-stirred mixture is pumped out at a slight faster rate of F_out = (F + f)...

Homework Statement Solve y' = y^2 - xy +1 \qquad(1) \qquad , using the substitution y = x + 1/u The Attempt at a Solution Upon substitution, I arrive at du/dx - xu = 1 which is linear/1st order/non-homogenous. When I apply the integrating factor method, I arrive at u(x) =...

Homework Statement Obtain solution valid near x=0 Homework Equations (x2+1)y''+6xy'+6y=0 The Attempt at a Solution y"+6x/(x2+1)y'+6x/(x2+1)=0 In representing the solution in series notation, I'm not sure how deal with the rational function because I know I need to have all of the x...

Homework Statement consider a lake that is stocked with walleye pike and that the pike population is governed by P'=.1P(1-P/10) where time is measured in days and P is thousands of fish. Suppose that fishing is started in this lake and that 100 fish are removed daily. modify the logistic model...

Homework Statement Solve the ODE: y'(x) = - \frac{y(x)}{\sqrt{a^2-y(x)^2}} The Attempt at a Solution To be honest I'm having trouble even classifying this ODE. My teacher hinted that the substitution z^2=a^2-y^2 could be helpful, but once I make the substitution, I can't seem to take the...

How do i solve this ODE, anyone have any ideas? \frac{dv}{dt} = g - \frac{b}{m}*v^2

Homework Statement Find the steady-state oscillation of the mass–spring system modeled by the given ODE. Show the details of your calculations. Homework Equations 1. y'' + 6y' + 8y = 130 cos 3t 2. 4y’’ + 8y’ + 13y = 8 sin 1.5t The Attempt at a Solution 1. cos(3t) at the end means the...

Homework Statement y' = y - x - 1, y(0) = 1, h = .25 Homework Equations The Attempt at a Solution y1 = 1+(.25)*(1-0-1) = 1 y2 = 1+(.25)*(1-1-1) = .75 This is not what the book has, but it is organized weird to me. It asks for EM twice, first w/ step size h=.25, then h=0.1...

Homework Statement I'm working on trying to first to solve an ODE on the form \sqrt{x(t)}\frac{dx}{dt} = 2\cdot t^2 My task is to find a solution on the form x(t) =nt^s The Attempt at a Solution I do some separation and I get that the above is equal to \sqrt{x(t)} dx = 2...

Homework Statement Hi I am trying to solve a seperable differential equation in Maple eqn1:=diff(x(t),t)=3*t^2/sqrt(x); But every time I type dsolve(eqn1,x(t)); I get the very hurtfull error from Maple "Error, (in ODEtools/info) x(t) and x cannot both appear in the given...

Homework Statement y' = ( y - 1 )^2 +0.01 y(0)=1 (trying out latex) y' = (y-2)^{2} + 0.01; y(0)=1 Homework Equations Separation of variables, Right? The Attempt at a Solution The solution is is y(x)=1+0.1 Tan (0.1x) How did they get this? I did separation of variables...

Homework Statement Hi I seem to remember that if you have a homogenous ODE y'' + p(t)y' + q(t)y = 0 which have the solutions y1 and y2. Where we are told that y1(t) \neq 0 then y1 and y2 are linear independent. I found the simular claim on sosmath.com but are they simply...

Homework Statement Solving the following differential equation with the given boundary conditions: \hbar^2 \frac{d^2}{dx^2}\psi (x) = 2mE\psi (x), \ \ \ \ \ \forall \ \hbar^2,\ m,\ E > 0 \psi(a) = \psi(-a) = 0 Homework Equations The Attempt at a Solution \hbar^2 \frac{d^2}{dx^2}\psi (x)...

I've been given a 2nd ODE in the form y'' + p(x)y' + q(x)y = 0 The equation does not satisfy the test for a unique solution at x_0 = 0, because p and q are not continuous at x_0 (both p and q have x in the denominator, so a value of 0 makes the function discontinuous). I've two...

I have a homework problem where I am to find y_2 for a 2nd ODE, with y_1=x. I'm familiar with the process of: let y_2 = ux y_2- = u'x u y_2'' = 2u' + u''x substituting these terms into the 2ODE, then letting u' = v. When integrating v and u' to solve for u, do I need to include...

Could you please help me or give me any hint to solve this ODE.. \frac{d^2y}{d x^2} + ( 2\rm{sech}^2 x - a^2 ) y = 0 where a is a constant. I want only even function solution. (y(x) = y(-x)) BTW, this is a homework problem. I encountered this equation while considering surface waves...

Homework Statement Solve first order ODEHomework Equations \frac{dy}{dx}=x^2+1+\frac{2}{x}y Rearranged \frac{dy}{dx}-\frac{2}{x}y=x^2+1 The Attempt at a Solution Integrating factor p=\exp(-\int \frac{2}{x})=\exp(-2\ln x)=x^{-2} Multiplying through by the integrating factor...

Homework Statement So I made a random differential equation to try to solve, but I found out that I can't solve second-order differential equations with knowledge I've gleaned solely from PF. So I need your help to ask how to solve this. Note that I've never taken a differential equations...

can anyone provide a Numerical algorithm to solve -y'' (x) +f(x)y(x) = \lambda _{n} y(x) with the boundary condition y(0)=y(a)=0 here 'a' is a parameter introduced at hand inside the program and f(x) is also introduced by hand in the program i am more interested in getting...

Homework Statement this is not from a math course, but from Gregory's classical mechanics book prob 2.10 it's easy to obtain the desired ODE \dot{r}^{2}=\frac{u^{2}}{a^{2}}(\frac{U^{2}a^{2}}{a^{2}}-r^{2}) since it's non-linear, i have a difficult time to solve for r(t) u, U and a are...

Homework Statement Hello, I should probably know how to do this, but I am confused as to how to solve the following 4th order ODE: \begin{align} & EI \frac{\mathrm{d}^4 w}{\mathrm{d} x^4} = 0 \\ & w|_{x = 0} = 0 \quad ; \quad \frac{\mathrm{d} w}{\mathrm{d} x}\bigg|_{x = 0} = 0...

Im having trouble with this question. can anyone explain please? Homework Statement y'' + 6y' + 9y = x*exp(-3x)3x Homework Equations Find the general solution.

Hi guy, I have this ODE that I'm having problems with y"+4y'+4y= e^(-2x)logx Now, Using method of UC to get rid of the RHS I've tried using Ae^(-2x) x^2 logx However, I'm not quite sure whether that is correct or not as I have never had a question containing logs before

Homework Statement Hi all, I'm trying to solve an ordinary differential equation. The problem is ty' + 2y = 4t^2 Homework Equations The Attempt at a Solution I got down to \int (t^{2})\frac{dy}{dt} [SIZE="4"]+ \int 2ty = \int 4t^{3} I am not sure about how to integrate the...

Hello, i have a bit of a problem with uderestanding how exactly we use RK4 method for solving 2nd order ODE. And last conversation with my proffesor only added up to my confiusion. Further more i couldn't find any example dealing with this problem if any1 could provide link explaining this...

As the tittle, can the 2nd ode (B.C not fixed, I need the general solution) y''-c/x*y=0 be solved exactly? Or can it be translated into some special mathphysical equations, such as Bessel? Hypergeometric? etc any comments or references are welcome. Thank you for advance!

Homework Statement By means of substitution x=X+1, y=Y+2 ,shwo that the equation dy/dx=(2x-y)/(x+2y+5) can be reduced to dY/dX=(2X-Y)/(X+2Y).Hence, find the general solution of the given equation. Homework Equations The Attempt at a Solution The first part is quite simple to...

First order nonlinear ODE -- Integrating factor + exact differentials, or not? Hello everyone, (I apologize if this did not format properly, if not I will attempt to edit it if that functionality is available upon submitting a question). I recently came across the following nonlinear ODE...

Hi, this is from a physics subforum of physicsforums: My calculus is not very good, but the above does not strike me as true and I would like a second opinion. If it is true, then my calculus is even worse than I thought and I need someone to explain to me how dr/dt=0 always implies that...

Homework Statement y'' + p(x)y' + q(x)y = 0 p(x), q(x) continuous for x = (-1,1)Homework Equations I. prove that if y1 is an answer to the ODE and y1(0) = y'1(0) = 0. then: y1 = 0 for all x = (-1,1). II. if y1 is an answer to the ODE, how would you find the second non-dependent...

I've been given the ODE: x^2 u''-x (x u'-u)=0 Solve. It's suppose to be an example in which a logarithmic term is required for the general solution. I would be glad if someone could look at what I've done and see if my solution is correct / incorrect. Thank you in advance for your time...

Given the ODE system: v' = u(u2-1) u' = v-u Define w=u2+v2. Compute w'. Find the largest radius R for which u2+v2<R so that the if the solution curve (u,v) is inside that circle the solution tends to (0,0) as t--> +\infty Any guidance would be appriciated !

Ly ≡ (x +1)^2y′′− 4(x +1)y′+6y =0 given y[1]=(x+1)^2 is a solution, use the ansatz y2(x)= u(x)(x+1)2 to reduce the order of the differential equation and find a second independent solution y2 how to reduce !? and i can't find u ...can't solve (x+1)^2u''+6u=0 please help! thx!

Homework Statement Find the solution to the ODE via the power series: y = \Sigma_{i=0} a_j x^{2j + m} Homework Equations y' - y^3 = 0 The Attempt at a Solution I get \Sigma_{i=0} a_j (2j+m) x^{2j+m-1} - \Sigma_{i=0} (a_j)^3 x^{3(2j + m)} = 0 I don't know how to deal with the cubic...

Homework Statement I'm working through the classic treatise on ODEs by Ince. I know that this is a somewhat dated text, but (imho) there are some real "gems" on the subject of ODEs here, well worthy of careful study. I'm looking at Problem #7 at the end of Chapter 1. In it, we are given a...

Reduce the equation (equation is attached) to a set of ODEs by the method of separation of variables. kindly help me with the solution, i m unable to solve.

Hi, so we just started learning about Laplace transforms yesterday, and I have a problem which I am not sure what to do: My question is about the second term, if it was a constant coefficient I could do this fine, but none of the 2 examples we did in class for solving ODEs with Laplace...

Homework Statement [PLAIN]http://img265.imageshack.us/img265/6778/complex.png I did the coefficient of the w' term. What about the w term? This seems like a fairly standard thing, but I can't seem to find it anywhere. What ansatz should I use for q, if the eqn is written w''+pw'+qw...

Homework Statement A mass m of 5 kg stretches a spring about 0.1m. This system is placed in a viscous fluid. Due to the fluid a braking force of 2N acts on the mass if the velocity is 0.04m/s. For the acceleration of gravity we can assume g = 10m/s^2. Set up from the balance of forces...