Odes Definition and 255 Threads

Hi! I think I have to ask this since I'm having health problems- from Kreyszig, for xy'=-y how do you verify the solution y=h(x)=clnx by differentiating y'=h'(x)=-clnx^2? I don't see how you get the x^2 term also for ODEs the solution is on an open interval a<x<b but how does it include...

I'm trying to optimize a system of 10-20 differential equations in Matlab using a genetic algorithm. The problem is, when I call the ode function, whether it be ode45, ode23, ode15, etc., it sometimes gets stuck in an infinite loop. The genetic algorithm no longer progresses and I have to Ctrl+C...

Homework Statement so I'm trying to find the general solution of this problem: \mathbf {x'} = \begin{bmatrix} 2 & 0\\0 & 2\end{bmatrix}\mathbf{x} Homework Equations det(A- rI) = 0 The Attempt at a Solution det(A - rI) = det \begin{bmatrix} 2-r & 0 \\ 0 & 2-r \end{bmatrix} =...

What kind of systems do ODEs describe? What kind of systems do PDEs describe?

Assuming knowledge of homogeneous ODEs and nonhomogeneous ODEs that can be made homogeneous (eg, y'-y=x), how does one solve those that cannot be made homogeneous (eg, y'-y=cosx, y''-xy'+y=0, cos(y'')+sin(y')=0)? EDIT: Maybe "made homogeneous" is the wrong way to put it... By being able to be...

Homework Statement Consider the IVP compromising the ODE. dy/dx = sin(y) subject to the initial condition y(X) = Y Without solving the problem, decide if this initial value problem is guaranteed to have a unique solution. If it does, determine whether the existence of that solution is...

I've started reading Gerald Teschl's Ordinary Differential Equations and Dynamical Systems. I'd desperately like to crack these definitions from section 1.2: classical ODE, linear, homogeneous, first order system, autonomous, as they seem pretty fundamental. My plan is to give answers to the...

Hi, could someone please link me to the relevant theorems etc (or explain personally) that answer the issue that follows. Say you have an ODE (let's say 2nd order for now). Let's look for a power series solution (ie assume we're engineers). So, we write out a couple of sigmas etc and sub...

Homework Statement (2xy-5)dx+(x^2+y^2)dy=0, y(3)=1 (2x+y^2)dx+4xy dy=0, y(1)=1 x^3y'+xy=x, y(1)=2 y'(t)=-4y+6y^3 We're doing these in 2nd yr engineering Math and I have heard the Lecturer say they are useful across all disciplines. I've heard him suggest RLC circuits, springs with...

Matrix Systems of ODEs -- Mathematica I'm trying to solve the classic "systemm of linear ODEs" of the form: Y(t)' = X*Y(t) Its homogenous, so it wouldn't hurt to rewrite it as Y(t)' - X*Y(t) = 0 (if that helps?) so here is my attempt at the solution solExp == NDSolve[Y'[t] ==...

Can anyone please suggest whether I can use MATLAB ode45 for the numerical solution of the following equations? mx ̈+ c_x x ̇ + k_x x= F_x0+ μ(v_r ) (K 〖VB〗^2 y ̇/v) sgn(v_r ) my ̈+ c_y y ̇+ k_y y= F_y0+ (K 〖VB〗^2 (y/v) ̇ ) Where, m, c_x, k_x, c_y, k_y, F_x0, F_y0, K, v are known...

i have a question but no mark scheme so i can't see where I am going wrong. a mass, m, is dropped with speed zero from point O at time t=0 after time t it has traveled x. the body is subject to acceleration due to gravity and drag -mkv. (A) write the equation of motion: ok so i know...

I've written a program to show the trajectory of a rocket around the Earth with initial conditions that can be manipulated to fix a circular or elliptical orbit. We start with Newton's 2nd law and use the equation a=F/m in freespace (so m can divide out) to get a 2nd order ODE and solve by...

Attempting Problem 1 of Arnold: ODEs, Ch. 1, section 2.2, it seems I'm not understanding something pretty basic about what he means by "the solution of a differential equation". This is the kind of equation he's talking about: \dot{x} = \mathbf{v}(x) \enspace\enspace\enspace (1) where, if...

I'm reading Arnold: Ordinary Differential Equations, Chapter 1. In section 1.2, an integral curve was defined as the graph, in the extended phase space, \mathbb{R} \times M, of the motion \phi : \mathbb{R} \rightarrow M of a phase point in M. In 2.2, an integral curve is defined as the graph of...

Hey, I feel kind of stupid for asking this, but how does one solve an ODE of the form y'' = 0 I know it's Ax+B=0 but I forgot how I got there. Cheers,

Are PDEs or ODEs more useful? Especially in biochemistry/molecular biology. Would learning PDEs also allow one to deal with ODEs?

Hey everyone. I'm trying to refresh myself of solving linear ODEs. For simplicity's sake, I began by trying to solve xy'=xy+y This is actually a separable ODE, and the solution is y = c_{1}xe^{x}. I am attempting to derive the same result from a series solution. First, rewrite this as a...

I am looking through my course notes for mathematical physics, in preparation for the exam, and I've run into a concept that I can't figure out. It comes up first when talking about the modified bessel's equation (x^2)y''+(x)y'-(x^2+p^2)y=0 And supposedly this can be transformed into...

Homework Statement I'm trying to solve the following system of ODEs. \alpha = \alpha (r) \alpha ' + \frac{n-1}{2r} \alpha =0 \alpha '' + \frac{n-1}{r} \alpha ' = 0 The attempt at a solution The solution to the first one is \alpha = r^{\frac{-(n-1)}{2} The solution to the...

Homework Statement I am asked to solve a coupled system of 5 ODEs. There is also a function, f, which describes the release of carbon dioxide over time. I am given the release rates at certain values of t and asked to interpolate for other values of t in the interval [1000 3000]. After...

Homework Statement I'm trying to solve the equations: \ddot{\phi} + 2\left(\frac{\cos \theta}{\sin \theta}\right) \dot{\theta}\dot{\phi} =0 and \ddot{\theta} - \sin \theta \cos \theta \dot{\phi^2} =0 for \theta(\lambda), \phi(\lambda) where the dots represent differentiation w.r.t...

I know that a 2nd order homo ordinary differential equation's solution is in the form of \[f(x) = {C_1}{e^{{a}t}} + {C_2}t{e^{{a}t}}\] for repeated real roots of the characteristic equation, and that the solution for a single complex root (and its conjugate) involves a cosine. I'm curious...

Homework Statement Solve this system of linear ODEs: 1) x''(t) = x + y 2) y''(t) = x + y Just fyi, this is part of a much larger problem but I need to solve this system! Homework Equations See above. The Attempt at a Solution Okay so I think the most logical way to solve...

Homework Statement Two identical masses m1 = m2 = m are connected by a massless spring with spring constant k. Mass m1 is attached to a support by another massless spring with spring constant 2k. The masses and springs lie along the horizontal x-axis on a smooth surface. The masses and...

Homework Statement 6x2(x+1)2y''+0.5x(x+2)y'+y=0 ii) Find all values of r for which there is a series solution of form xr\sum(anxn,n=0,inf) a0 \neq0 Find all values of r for which there is a series solution of form inf xr\suman(x-2)n...

How to solve two nonlinear ODEs with boundary conditions? Here is the Q:

Can anyone help me to get the general solution of the linear partial differential equations with variable coefficients of any order?

Homework Statement Solve (x - \sqrt{xy})dy - ydx = 0 Rearranged gives us -y + (x - \sqrt{xy})y' = 0 And it looks like an exact differential equation, but is it really? Homework Equations For any given exact equation of the form M(x,y) + N(x,y)y' = 0 The following must be true...

I have been working on a derivation in which the following simultateous ordinary differential equations have appeared: f^{(4)}(x)-2 a^2 f''(x)+a^4 f(x)+b(g''(x)-a^2 g(x))=0, g^{(4)}(x)-2 a^2 g''(x)+a^4 g(x)-b(f''(x)-a^2 f(x))=0, where a and b are constants. I figured that I could solve...

Ok, so I've been studying the method of variation of parameters in order to solve 2nd order ODEs, and I have a question regarding a supposition that is made in the definition of the method. Say, y'' + p(t)y' + q(t)y = g(t) Then the general solution to the above equation is c_1y_1(t) +...

Homework Statement I need to annihilate ln(x) Homework Equations The Attempt at a Solution my try was saying that this is a eular equation with r1=r2=0 c1=0 and c2=1 so the annihilator should be D^2 but I don't think it works. Any other suggestions ? Thanks.

Homework Statement In a problem I was given a system of three differential equations concerning three functions, x(t), y(t) and z(t): dx(t)=2y(t)dt, dy(t)=[z(t)-x(t)]dt, dz(t)=[c^2x(t)-2y(t)]dt. (where c is a constant) The problem asked me to prove that when t is large, x(t)+z(t)...

Hello All, I am stuck on the following question. Can you please help to find the solutions Using the complementary function and particular integral method, find the solution of the diffential equation which satisfies y(0) = 1 and y'(0) = 0. y'' + 3y' + 2y = 20cos2x and then can you...

Homework Statement I have a problem in solving a system of two ODEs for BVP 1. Pb is function of X & A 2. A is a function of X,Pb,A 3. BCs are X = 1, Pb = 0, A = 0.441 X = 0, Pb = 0 Q is a variable to achieve the other end BC I have tried to use ODE...

I have a somewhat theoretical question regarding Differential Equations: How can we reconcile the fact that if I go from let's say this system of 1st ODE x' = 2y-x y' = -x+y to a 2nd ODE "using x(t) instead of y(t)" we get: x" + x =0 then back to a system of 1st ODE: letting...

Could someone explain why the graph of a solution can never cross a critical point?

1. Using the complementary function and particular integral method find the solutio of the differential equation. d2y/dx^2 + 3 dy/dx +2y = 20cos2x Which satisfies y(0) = 1 y'(0) = 0 Homework Equations The Attempt at a Solution

Homework Statement How can I annihilate the following ? 4e-2t*cos(2t) Homework Equations The Attempt at a Solution I know that if I want to annihilate e-t it would be (D-1) and to annihilate cos(2t) it would be (D2+22) but what happens if they are multiplied ? how do I...

I want to know if there is a general solution to a second order homogeneous differential equation with variable coefficients?

Homework Statement 1)Find the solution of x'=x^{\frac{1}{2}} that passes through the point (t_0, x_0) where x_0>0. 2)Find all the solutions of this equation that pass through the point (t_0,0). Homework Equations Direct integration. The Attempt at a Solution...

Hello. I took a class on ODEs and learned about solving second order homologous equations by writing down the characteristic equation. http://www.sosmath.com/diffeq/second/constantcof/constantcof.html I am now learning about PDEs on my own and I came across parabolic, hyperbolic, and...

Homework Statement Verify that the differential operator defined by L[y] = y(n) + p1(t)y(n−1) +· · ·+ pn(t)y is a linear differential operator. That is, show that L[c1y1+ c2 y2] = c1L[y1] + c2L[y2], where y1 and y2 are n times differentiable functions and c1 and c2 are arbitrary...

Hi guys, I really have no idea how to approach finding the particular integral for, say: f'' + 5f' + f= e^x sinx Could anyone help me? And for future reference how do you go about finding the PI for any combination of polynomials/exponentials/sinusoidals? Thanks in advance for the help!

I have the following coupled ODE: 2x+y^2=d^2x/dt^2 2y+x^2=d^2y/dt^2 How would one solve for x(t), y(t)?

Hi guys, i have 4-coupled ode's that are giving trouble (1) \frac{dy_1}{dt}=y_2y_3-\mu y_1, \hspace{1cm} \\(2) \frac{dy_2}{dt}=y_1y_4-\mu y_2, \hspace{1cm} \\(3) \frac{dy_3}{dt}=1-y_1y_2, \hspace{1cm} \\(4) \frac{dy_4}{dt}=1-y_1y_2 I need to show that the steady state solutions are y_1=\pm...

Finding the integrating factor (ODEs) [Solved] Working on this problem, I can't figure out why we take the derivative of \mu with respect to y, and what to do when our integrating factor is a function of both x and y. In the case below, it ended up being separable, but what can you do if it's...

Homework Statement I'm trying to solve a set of boundary value ODEs numerically, which contains about ten parameters. And i found that with some values of parameters, the solution may be singular at an endpoint(Maple says "system is singular at the righthand endpoint"). So i guess there...

Hi there I have been trying to set up a system of ODEs that are ultimately a solution to Burgers equation with a source term, and it boils down to: x' = 11v v' = f(H,H_x,s,s_x) where x = x(t), H = H(x,t), s = s(x) and H_x,s_x are the partial derivatives wrtx. The problem comes that I do...

I have learned Calculus (single and multi-variable) Ordinary Differential equations (upto 2nd order linear with Laplace transforms, including Dirac Delta functions and Fourier Series. I have not learned series solutions nor special functions which I see is the next step in this chapter)...