Ode Definition and 1000 Threads

I struggle to solve this Differential equation: x^2y' +2xy = arctanx What I did was just divide x^2 on both side of the sign of equality in order to get the same form as a first-order linear diff.equation. After I've done that, I just multiply e^(2lnx) on the both side of the equation so...

Hi, have this strange 2nd order ODE in one of my tutorials that I am struggling to start. I am not used to dealing with derivatives of both x and y as well as a function involving t. I was wondering if anyone may be able to point me to the starting line. I am trying to convert them into 1st...

Every second order linear ODE a(x)y''+b(x)y'+c(x)y=F(x) can be transformed into the forms; u''+g(x)u=h(x) divide whole equation to a(x) and choose y(x)=u(x)^(e^s(x)) but how i choose s(x) ?Please help...

Hi, I have a coupled system of ODE like: w1'' = A w2'' + B w1 + C w2 w2'' = D w1'' + E w1 + F w2 I need to solve it analytically but it seems it cannot be solved using eigenvalue method. My concern is first that if this system have sufficient equations and if so how it can be solved...

Hi, I posted this on the homework forum, but I haven't gotten any responses there. I thought there might be a better chance here. 1. Homework Statement I have the ODE h'' + h'/r + λ2h = 1, where h = h(r), and I want to find h(r). 2. Homework Equations The corresponding...

I have a third order, non-linear, homogeneous, constant coefficient ODE that I need to solve but have no idea how to do it. To make matters worse, one of the boundary conditions are indefinite. Here's the equation, y''' + y*y'' - y'^2 + 1 = 0 and the BC's y(0) = 0 y'(0) = 0 y'(\infty) =...

Homework Statement I have the ODE h'' + h'/r + λ2h = 1, where h = h(r), and I want to find h(r). Homework Equations The corresponding homogeneous equation is a Bessel equation that has the solution hh = c1J0(λr) + c2Y0(λr), where J0 and Y0 are Bessel functions. Now I was planning on using...

Homework Statement A car, of mass 720kg, moves along a straight horizontal road. The engine of the car exerts a constant power of 81kW. The car experiences a resistance to motion which has magnitude 90v N, where v ms^-1 is the speed of the car at time t s (a) Show that v satisfies the...

Hi 2 all Necessary i need ode that's have no general sol nd I need also an ode that's i can solve it with more way i hope 2 found it .. thanks all i w8

I attached scans of the questions rather that typing it all here. It's also easier to read. Questions: http://img4.imageshack.us/img4/9306/33991727.th.jpg Attached Reference Materials: http://img40.imageshack.us/img40/6599/74821170.th.jpg

Homework Statement Find a continuous y(t) for t > 0 to the initial value prob: y'(t)+p(t)y(t)=0, y(0)=1 where p(t)=2 for 0 < t < 1 p(t)=1 for t > 1 and determine if the soln is unique. The Attempt at a Solution By standard ODE techniques I arrive at y=\exp(-2t) for 0 < t < 1 y=\exp(-t)...

Homework Statement Use a Green's function to solve: u" + 2u' + u = e-x with u(0) = 0 and u(1) = 1 on 0\leqx\leq1 Homework Equations This from the lecture notes in my course: The Attempt at a Solution Solving for the homogeneous equation first: u" + 2u' + u = 0...

Solve using laplace. The diff eq is y'' + 2*y' + *y = 0 subject to y(0)=1 and y(pi)=0 Sorry if notation isn't the norm. y'' and y' and y are time (t) based functions.

Homework Statement y'(t) = (y-5t)/(y+t) IVP: y(1)=0 Homework Equations M(x,y)dx+N(x,y)dy = 0 - or do i use - y'+p(x)y=q(x) The Attempt at a Solution Well I used the first equation (with M and N): 1. first checked that it was exact, by taking the partial of M and N with respect to y and t...

Given the equation y'= xg(x,y) , suppose that g and (partial) dg/dy are defined and continuous for all (x,y). Show the following: 1) y(x)=0 is a solution 2)if y=y(x), x in (a,b) is a solution and if y(x0)>0, x0 in (a,b), then y(x)>0 for all x in (a,b) Please i need your help.

Homework Statement A curved mirror of equation y=y(x) has that property that whenever a ray of light emanates from the origin it reflects parallel to the x-axis. Find the equation of the mirror Don't even know how to get started on this, Don't need a solution just need some starting hints...

Homework Statement dx/dt = x - y + (x^2) - xy dy/dt = -y + (x^2) - Determine the critical points for the equation, - Determine the linearized system for each critical point and discuss whether it can be used to approximate the behaviour of the non-linear system. What is the type and...

Homework Statement I'm working with a heat equation that requires a Laplace transform. I performed the transform and ended up with a basic ODE with a particular solution. I solved for the particular solution and then realized I was working on an infinite domain in my spatial dimension...

Homework Statement Given the ODE \frac{dy}{dt} = y \cdot t^{-1} -2y^2 Find all the maximal solutions defined on the interval (0,\infty) \times \mathbb{R}. Homework Equations The Attempt at a Solution This looks like a Bernoulii equation I find the general solution to...

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.

Homework Statement Use finite difference central method to approximate the second-order Ordinary Differential Equation U''(x) = e^x over domain [0, 1] where: u(1) = 0 (Dirichlet Bound) U'(0) = 0 (Neumann Bound) Homework Equations let 'h' be the change in x direction The Attempt...

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 \left(\frac{dy}{dx}\right)^2 - 4x\frac{dy}{dx} + 6y = 0 Homework Equations A common approach we have used for similar problems has been to let P = dy/dxThe Attempt at a Solution Doing so we have: P^2 - 4xP +6y = 0 \Rightarrow 6y = 4P(x - P) Differentiating gives: 6P...

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 Given an ODE h(y(t)) \frac{dy}{dt} = q(t) How do I define the maximal solution of this equation? According to my textbook for this course a maximal solution for the above problem if it cannot be obtained from another solution as a restriction to a smaller...

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)...

Have been struggling with errors galore on this one. I am not too conversant with ODEs in MATLAB. The problem is as follows. I have to solve these two ODEs for A1 and A2. A1dot = k2*A2 - k1*A1 - k3*A1/(k4 + A1) + R A2dot = k1*A1 - k2*A2 Here R is a function of time defined as follows...

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...