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.
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...
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...
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...
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) \\...
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...
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}...
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} &...
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...
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...
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...
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...
{\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...
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)...
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...