Ode Definition and 1000 Threads

  1. A

    Solve an ODE using exact methods?

    Homework Statement dy/dx + 0.8 y = 0.6 e ^-(0.6+0.8) , y(0) = 1 Solve this ordinary differential equation subject to the given condition using exact methods and evaluate the solution y for x = 0.0 (0.05) 0.5, i.e from x = 0 to x = 0.5 in steps of 0.05). Hi, am pretty...
  2. A

    Solving ODE with Transcendental Function: e^{x-y'}

    Homework Statement y' = e^{x-y'} The Attempt at a Solution I have no idea how to handle the situation when y' is appeared in the input of a transcendental function. I substituted y'=p to try to find a parameterized solution to this ODE but it leaded me to nowhere.
  3. A

    A challenging ODE question: find an integrating factor

    This is the ODE: y' + siny + xcosy + x = 0. The problem is: Find an integrating factor for the ODE above. You can see my solution to the ODE here: https://www.physicsforums.com/showthread.php?t=543662. from my solution it seems that e^x(sec^2(y/2)) must be an integrating factor. but I fail...
  4. Y

    ODE System with Variable Coefficients

    hi suppose we have this equation : d/dt(X)=A(t)*X x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients. coefficients of equations and consequently A are depend on t which is time. how i Solve this equation ? thanks
  5. QuarkCharmer

    Multivariable Calc topics required for ODE?

    My school requires Calculus III before DEQ, though I had the department allow me to take the two concurrently. I am wondering what Calc III topics I should be fluent into prepare for Differential Equations. I'm sure this university teaches DEQ with an understood previous knowledge in...
  6. J

    Forming a matrix using Euler's method and ODE

    L is the operator. Lx=x'(t)+u(t) x(t) =0. Provided that x(t0)=x0. Before writing the matrix. The book express it out in equations. x(t0)==x0 x(t1)-x(t0)+Δt u(t0) x(t0)==0 x(t2)-x(t1)+Δt u(t1) x(t1)==0 ... Euler's method is x(t0)+Δt f[x0,t0], right? so where did the x'(t) from the...
  7. A

    Is My Solution to the ODE Using Weierstrauss Substitutions Correct?

    Homework Statement y' + siny + xcosy + x = 0 The Attempt at a Solution well, I've used Weierstrauss substitutions: siny = 2t/(1+t^2) , cosy = (1-t^2)/(1+t^2) , dy = 2dt/(1+t^2) where t=tan(x/2). 2/(1+t^2)dt + 2t/(1+t^2)dx + x(1-t^2)/(1+t^2)dx + xdx = 0 2dt + 2tdx + x(1-t^2)dx +...
  8. M

    Non linear pde need to change it to an ode

    Homework Statement my non linear pde is du/dt = d/dx [3u2 - d2u/dx2 ] The question says to let u(x,t) = f(x-ct) Where the function f tends to 0, f' tends to 0 and f'' tends to 0 but the (x-ct) tends to positive or negative infinity. Homework Equations i thought the solution was to find...
  9. A

    Solving ODE: 2y(1+x^2√y)dx + x(2+x^2√y)dy = 0 | Step-by-Step Guide

    Homework Statement 2y(1+x^2\sqrt{y})dx + x(2+x^2\sqrt{y})dy = 0 The Attempt at a Solution well, I substituted x^2√y=u but then when I tried to differentiate it I understood it would be so hard. Please check and see if I've differentiated it correctly: √y = u/x^2 -> y = u^2.x^-4 -> dy/dx =...
  10. L

    Solving 2nd Order ODE: du/ds & k^2

    d^{2}u/ds^{2}= cosu[(du/ds)^{2} - k^{2}]
  11. D

    Stability of Equilibrium solutions to ODE

    Homework Statement y'=(1-y)(3-y)(5-t) Homework Equations find equilibrium solutions of ODE and determine their stability The Attempt at a Solution equilibrium solutions are y = 1 and y = 3, I'm not sure how to determine their stability without some form of a slope field, is it...
  12. A

    How Do You Solve This Challenging Separable ODE Problem?

    Homework Statement solve y(xy+1)dx + x(1+x^2y^2)dy=0 The Attempt at a Solution well, I substituted u=xy. Here is what I've done so far. du = xdy + ydx -> xdy= du - ydx -> xdy = du - (u/x)dx (u/x)(u+1)dx + x(1+u^2)dy=0 (u/x)(u+1)dx + (1 + u^2)(du - (u/x)dx)=0 (u^2/x)dx + (u/x)dx +...
  13. B

    Ode 2nd degree with a polynomial as a coefficient

    Hi friends, I have been trying to solve the ode of second degree below with respect to z: d2y/dz2=(i/a*z+b)*y i is the complex i, a and b are constants i ended up with the summation of bessel functions of first end second kind. Then I checked with MATLAB ode solver it gives no...
  14. B

    MATLAB Solving a Complex Second-Degree Ode with Bessel Functions | MATLAB Help

    Hi friends, I have been trying to solve the ode of second degree below: d2y/dz2=(i/a*z+b)*y i is the complex i, a and b are constants i ended up with the summation of bessel functions of first end second kind. Then I checked with MATLAB ode solver it gives no explicit solution...
  15. R

    How much math is needed before taking ODE?

    I am a junior in high school taking AP Calc AB. This is the highest level of math offered at my high school (everyone else in my class is a senior) I want to start taking math classes at my community college. Currently I take College Chemistry I there (fall semester) and it's going very well...
  16. G

    Solve 1st Order ODE: Need Help | Math Forum

    [PLAIN]http://img440.imageshack.us/img440/7352/11unled.jpg Having some trouble. I am not sure what d_t(u) and :u(with the . above it) means. Would appreciate some help. Thanks
  17. G

    Can PDEs be solved using ODEs in quantum mechanics?

    Here's my question: as soon as I learned Quantum Mechanics and Schrodinger equation, I saw a "similarity" with the equation one gets in classical mechanics for the evolution of a function in phase space. In QM one has: i\hbar\frac{d}{dt}\psi = \hat{H}\psi and this is a evolution...
  18. E

    What Do ODE, PDE, DDE, SDE, and DAE Stand For?

    Okay, kind of a silly question...but what do all of these stand for? ODE=Ordinary Differential Equations ( ;O I hope this is right, I took a course on this stuff) PDE=Partial Differential Equations ( Hope this is right too, taking this next semster) DDE=...? SDE=...? DAE=...
  19. Q

    How Can Initial Conditions for Parallel ODE Solvers Be Refined for Accuracy?

    I wish to solve the following DE numerically on the interval t:[0,a] using parallel processors. Given y'(t)=f(t,y) and y(0)=y0. One way to parallelise the DE is to split the interval [0,a] into n subintervals [ak/n, a(k+1)/n] where k = {0,1,...,n-1}. Problem: I need to know the initial...
  20. X

    2nd basis function for 2nd order ODE

    i have the first solution y_1(t) = t for (1-t)y'' + ty' - y = 0. I need to get the 2nd linearly independent using Abels theorem. the integration is messy but i have it set up (sorry no latex); y_2 = (t) * integral to t ( 1/s^2 * exp( -integral to t (s(s+1) ds) ) ds. Could anyone...
  21. N

    Solve 1st Order ODE: x^2+y^2+2xy+y^2+(x^3/3)dy/dx=0

    i have this differential equation of the first order [x^2+y^2]+[2xy+y^2+(x^3/3)]dy/dx=0 i tried to solve it by substitution putting x^2+y^2=v ,but it doesn't work also it is not exact or homogeneus to solve it by these methods. I still believe it can be solved using substitution but i can't...
  22. A

    ODE - having trouble using method of undetermined coefficients

    Homework Statement Find a particular solution. 1. y'' +4y = 4 cos (2t) (for this problem, the instructions tell me that the forcing term is a solution of the associated homogeneous solution) 2. y'' + 16 y = 3 sin (4t) Homework Equations The Attempt at a Solution 1. I guess...
  23. N

    Solving Linear ODE: 2*dy/dx - y = e^x at y(0) = 0

    Homework Statement Solve 2*dy/dx - y = e^x at y(0) = 0 The Attempt at a Solution So the integrating factor is e^-x Multiplying through by e^-x: 2e^-x(dy/dx) - ye^-x = 1 Now this is where I'm having a slight problem, isn't the left hand side meant to contract via the product...
  24. B

    FT to solve 2nd order ODE; only one solution

    If I solve a simple 2nd order ODE using a Fourier transform, I only get one solution. E.g.: \frac{d^2f}{dx^2}=\delta (2\pi ik)^2\tilde{f}=1 \tilde{f}=\frac{1}{(2\pi ik)^2} f = \frac{1}{2}xsgn(x) However, the general solution is f = \frac{1}{2}xsgn(x) + Cx + D Why do I...
  25. J

    Forgotten my maths Simple 1D ODE, spherical coordinates

    Hi, I seem to have forgotten some of my math how-to, as I haven't done this in a while. Looking through my notes, Bird, Stewart and Lightfoot, Greenberg, etc. don't really help. My equation is this, at steady state: 0 = 1/r^2 ∂/∂r (D*r^2 ∂C/∂r) + P Where P is some production rate...
  26. R

    Hydrogeology - setting up ODE for tank problem

    Hi there. I have trouble setting up an ODE for a hydrogeologi problem. I have attached the problem and my answers as pdf as they contain diagrams and graphs to help describe the problem. Hope that someone can/will help me. :-) Thank you. -Rasmus1. The problem is attached in Eng04-2010.pdf 2...
  27. X

    Derivation of Solution to nonlinear 2nd Order ODE

    I need to derive the solution for the differential equation analytically: y'' + g(t,y(t)) = 0 y'(0) = z_o y(0) = y_o I know the solution is: y(t) = y_o + z_ot - single integral from 0 to t of (t-s)g(s,y(s))ds I believe I need to assume something about the solution being a function...
  28. D

    Particular Solutions for Non-Homogeneous Differential Equations

    Find a particular solution for the following non-homogeneous di eren- tial equation by the method of undetermined coefficients: a. y'' + 8y' +12y = e^-2x + sin(2x) b. y'' + 11y' - 12y = 3x^2 + 4 + e^x I got for a. Yp(x) = 1/4xe^-2x + 1/40cos(2x) +1/20 sin(2x) b. Yp(x) = -1/4x^2...
  29. J

    Verifying phi(x) is an explicit solutionDomain = RInterval: x>=-2

    Just started Engineering Math III and have a question. Sorry about the notation, our library computers have scripts disabled. My math prof does a poor job of explaining the concepts. Help me out! Homework Statement Verify the indicated function y=phi(x) is an explicit solution of the...
  30. S

    Solve 1st Order ODE: xyy'=x^2+3y^2, y(1)=2

    Homework Statement Find the following IVP Diff.Eq. xyy'=x^2+3y^2 y(1)=2 Homework Equations The Attempt at a Solution I've been struggling with this problem for a while now. I believe I have figured out it is homogenous, thus y=ux substitution applies. Through some work I have arrived at...
  31. R

    Existence, Uniqueness of a 1st Order Linear ODE

    Homework Statement Solve the Cauchy problem: (t2 + 1)y' + etsin(t) y = sin(t) t2 y(0) = 0 Homework Equations y'(t,y) + p(t)y = g(t,y) Integrating factor e(integral of p(t)) The Attempt at a Solution I tried finding an integrating factor, but it came out ugly. I couldn't solve the...
  32. T

    How Is Equilibrium Price Stability Determined in Market Dynamics?

    Homework Statement In the market for a certain good, the price p(t) adjusts continuously in the presence of excess supply or demand: \frac{dp}{dt} = F(D(p)-S(p)) where F(0) = 0, F'>0. Obtain the condition for stability of the equilibrium price p* in terms of the slopes D'(p*) and S'(p*), and...
  33. Jonnyb42

    ODE, bernoulli equation -> leads to crazy integral

    ODE, bernoulli equation --> leads to crazy integral ! Homework Statement An Initial Value Problem, ODE (Bernoulli equation) ODE: [x^2]*y' + 2*[x^3]*y = [y^2]*(1+2*[x^2]) IV: y(1) = 1/2 Homework Equations general form of Bernoulli's equation: y' + a(x)y = b(x)*[y^n] First...
  34. Y

    Analysing Lotka and Volterra equation (ODE)

    Hello everyone, I am working on a project on basically about ODE and phase plane and I am working on this paper by Hanski http://www.arctic-predators.uit.no/biblio_IPYappl/HanskiNature93%20mustelid%20predators.pdf How do i find numerical solutions which methods should I use ...
  35. Jonnyb42

    Simple ODE problem, Bernoulli's Equation

    [SOLVED] simple ODE problem, Bernoulli's Equation Homework Statement Initial value problem: Relation: t*y' - 2*[t^2]*sqrt(y) = 4*y Initial value: y(1) = 4 Homework Equations general form of Bernoulli's equation: y' + a(t)y = b(t)*[y^n] First order, linear ODE form: y'...
  36. O

    Rawr Stuck on ODE (linear 1st order)

    Homework Statement Solve the initial value problem: y'+\frac{4y}{x+8}=(x+8)^{8} , y(0)=8. The differential equation is linear. Homework Equations N/A The Attempt at a Solution I can see that the equation is in the form y' +P(x)*y = Q(x) so I'm like "easy, let me get an...
  37. T

    Break Second order ODE into a system of first order ODE's

    Homework Statement I haven't done this for several years and have forgotten. Kicking myself now over it since it looks like something so simple but i cannot figure it out... I need to break this second order ODE into a system of first order ODE's in matrix form to use within a crank...
  38. A

    Solving ODE: (xy^2 + y^2)dx + xdy = 0 - Exact Solutions

    (xy2+y2)dx + xdy = 0 the questions are: a. Show that the equations above can be an exact differential equations! b. Determine its solutions! Help me please because i have working on it for 3 hours and i can't find its integration factor to change the un-exact differential equation...
  39. N

    Solving Linear ODE: dy/dx-2y=x^2e^2x

    Homework Statement Solve \frac{dy}{dx} - 2y = x^{2}e^{2x} The Attempt at a Solution Integrating factor = e^{2x} So we multiply through the given equation by the integrating factor and get: e^{2x}\frac{dy}{dx} - 2e^{2x}y = x^{2}e^{4x} Contract the left-hand side via the chain rule to get...
  40. G

    Write down the ode satisfied by a characteristic curve

    Homework Statement i)write down the general form of a semi lenear first order pde in the unknown u(x,y) ii)write down the ode satisfied by a characteristic curve in the x-y plane for your pde ii)give a careful derivation of the ode satisfied by u(x,y) along such a charcteristic curve...
  41. M

    How Do You Solve This First Order ODE with Given Condition?

    The question is x^2dy/dx + y^2=0 , y(1)=3 I re-arrange the equation to get -1/y^2dy=1/x^2dx Seperated them, then I integrate both sides to get 1/y=-1/x + c Now I don't get how they got the answer y=3x/(4x-3), as when I try use the condition I get a different answer, could anyone help? I...
  42. I

    Non-linear 2nd ODE involving squares of derivatives

    Homework Statement y''+(1/y)*(y')2=0 Homework Equations The Attempt at a Solution This is another problem I am having trouble with. I have done searches around the internet, but seen that all "non linear" ODE of second order involves a non linear form in a non differential term...
  43. I

    Checking answer vs. mathematica (2nd order equidimensional non homog. ODE)

    Homework Statement Obtain general solution: x^2 y''(x)-2 x y'(x)+2 y(x) = x^2+2 Homework Equations Using Euler Cauchy method, and using variation of parameters The Attempt at a Solution Hey all, I have been struggling with this problem since yesterday in obtaining the...
  44. J

    Solving nonlinear ODE with ODE45 fails at bifurcation point?

    Hello everybody, Background and problem description I have derived an analytical expression for an implicit frequency response function. To verify it, I would like to check with a numerical solution. For very weak nonlinearities, congruence is obtained. For weak nonlinearities, the...
  45. J

    Solving a 2nd-Order ODE for Conservation of Energy

    Homework Statement Consider a mechanical system describe by the conservative 2nd-order ODE \frac{\partial^{2}x}{\partial t^{2}}=f(x) (which could be non linear). If the potential energy is V(x)=-\int^{x}_{0} f(\xi) d \xi, show that the system satisfies conservation of energy...
  46. Telemachus

    Finding the Curve that Satisfies a Geometric ODE

    Hi there. I have this exercise in my practice for differential equations, and it asks me to find the curve that satisfice for every point (on the xy plane) the distance from (x,y) to the points of intersection for the tangent line and the x axis, and the normal with the x-axis remains constant...
  47. K

    How to solve ODE for independent function

    Hello, I need to solve numerically an equation of the form v(t) = k1*z(t)*w(t)-k2*i(t)-k3*di(t)/dt The issue is that rungekutta methods are useful for solving di(t)/dt = 1/k3 * [ k1*z(t)*w(t)-k2*i(t)-k3*-v(t) ] but I need to solve for v(t) What I did was: v...
  48. S

    Why is Green's function method for ODEs only considered for x < z?

    Homework Statement I'm teaching myself the Green's function method for ODEs, because it looks relevant to my interests. This is a (slightly contrived) problem I just came up with arbitrarily: y''+5y'+6y=sin(x) \; \; \; ; \; \; \; y(0)=y'(0)=0 Homework Equations i) When considered as a...
  49. M

    Second order ODE initial value problem

    So the question is y" - y' - 6y = e^-x + 12x, y(0)=1,y'(0)=-2 First I found the general solution which came out to be, Ae^3x + Be^-2x I then Substituted y=ae^-x + bx + c y'=-ae^-x + b y"=ae^-x Then I just compared the coefficients to get a=-1/4, B=-2 and C=-1/6 So I am getting y =...
  50. M

    Linear second order non-homogeneous ODE question

    Determine the general solution to the ODE: y'' + 2y' = 1 + xe-2x I know the solution will be of the form y = yh + yp. The homogeneous solution is y = c1 + c2e-2x. For the particular solution, I have been using the method of undetermined coefficients. c3e-2x won't work as it is not...
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