What is System of ode: Definition and 14 Discussions

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.

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  1. Ketav

    Solving a System of 2 ODES with Interval conditions

    Homework Statement I am trying to solve a system of 2 ordinary differential equations using matlab. However, I am not able to get numerical solutions from the code despite having keyed in all possible solutions. Homework Equations The equations I am given are: dx/dt=A(x/t)+By...
  2. T

    Finding a Solution to a System of Differential Equations

    Homework Statement Find a solution \bf{\phi} of the system $$y'_1(t)=y_1(t)+y_2(t)+f(t)$$ $$y'_2(t)=y_1(t)+y_2(t)$$ where f(t) is a continuous function $$\bf{\phi} (0)=(0,0)$$ Homework Equations A hint was given to define ##v(t)=y_1(t)+y_2(t)## The Attempt at a Solution Using the suggested...
  3. B

    Solving a System of ODE for Steady State

    I am trying to find the steady states in the ODE system. Assuming y0 = 2.5 * 10^5, I want to calculate y1, y2, y3 at the steady state. I do not understand how this would be possible, because only y0 is given and the following: d0 = 0.003, d1 = 0.008, d2 = 0.05, d3 = 1, ry = 0.008, ay = 1.6/100...
  4. W

    Can Euler Forward or 4th Order Runge-Kutta Methods Approximate Systems of ODEs?

    My question is about whether it's possible to use the Euler Forward or 4th order Runge-Kutta Methods to approximate the following system ( where the differential of other equations are on the right hand side) : $$ \begin{cases} \frac{dy_1}{dt} = f_1(y_1,y_2,y'_2, ... , y_n, y'_n, t) \\...
  5. D

    System of ODE - comparison with paper

    I have the following system of differential equations, for the functions ##A(r)## and ##B(r)##: ##A'-\frac{m}{r}A=(\epsilon+1)B## and ##-B' -\frac{m+1}{r}B=(\epsilon-1)A## ##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a...
  6. B

    Physical interpretation for system of ODE

    If an ODE of 2nd order like this A y''(x) + B y'(x) + C y(x) = 0 has how physical/electrical interpretation a RLC circuit, so, how is the electrical interpretation of a system of ODE of 1nd and 2nd order? \begin{bmatrix} \frac{d x}{dt}\\ \frac{d y}{dt} \end{bmatrix} = \begin{bmatrix}...
  7. B

    How to reduce a system of second order ODEs to four first order equations?

    Someone can explain me how to get the general solution for this system of ODE of second order with constant coeficients: \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} \frac{d^2x}{dt^2}\\ \frac{d^2y}{dt^2}\\ \end{bmatrix} + \begin{bmatrix} b_{11} &...
  8. A

    MATLAB Critical points of system of ODE in MATLAB - Game theory and poker

    Hello there, I hope I'm posting in the right section. I have been doing some work on evolutionary game theory and poker. I will give a brief description of how I got here. I have eight strategies i = 1, 2, \ldots, 8 and the eight proportions of the population playing each strategy is...
  9. C

    Solving a system of ODE with multiple 'time' variables

    Homework Statement Hi everyone, Consider the following system of (first order) differential equations: \dot{x}=f(t_1,x,y,z) \dot{y}=g(t_2,x,y,z) \dot{z}=h(t_3,x,y,z) where \dot{x}=\frac{\partial x}{\partial t_1}, \dot{y}=\frac{\partial y}{\partial t_2}, and \dot{z}=\frac{\partial...
  10. I

    Solving a Non-Linear System of Differential Equations

    Homework Statement assuming dy/dt = Dy, d^2y/dt^2 =D^2, etc: determine the general and particular solutions to the following linear pair of differential equations: 2D^2y-Dy-4x=2t 2Dx-4Dy-3y=0 Homework Equations The Attempt at a Solution I have went through algebraic...
  11. F

    System of ODE for functions with different origins

    Hi, I have a system of coupled ODE like: a1 * Y1" + a2 * Y2" + b1 * Y1 + b2 * Y2 = 0 a2 * Y1" + a3 * Y2" + b2 * Y1 + b3 * Y2 = 0 I know for example by eigenvalue method I can solve it, but here is the issue: Y1 = f1 (x - a) and Y2 = f2 ( x - b). In the other word there is a shift...
  12. T

    System of ODE Boundary Value Problem with 2nd Order Backward Difference

    {\frac {{\it du}}{{\it dx}}}=998\,u+1998\,v {\frac {{\it dv}}{{\it dx}}}=-999\,u-1999\,v u \left( 0 \right) =1 v \left( 0 \right) =0 0<x<10 Second Order Backward Difference formula {\frac {f_{{k-2}}-4\,f_{{k-1}}+3f_{{k}}}{h}} I'm trying solve this numerically in matlab, but can't seem to...
  13. A

    Interesting system of ODE, application in physics?

    Hi all, I have a project to do for system of ordinal differential equations and their applications in physics. One of my tasks is to find where in physics the following system of ordinal differential equations appear: dA1(x)/dx=f(x).A2(x) dA2(x)/dx=f(x).A1(x)+ h(x).A2(x)+ g(x).A3(x)...
  14. G

    Solving System of First-Order ODEs: Exact Solution for x(t)

    Dear all, I have been trying to solve the following system of first-order ordinary differential equations for a week: x' = y * (a1*x + a2*y + c1), y' = y * (a3*x + a4*y + c2), where x and y are functions of t, and ai and ci are constants. This system seems not very complex, but I have not...