Question

Applications of simultaneous differential equations

Answer 1

dontttt. nooooooooo......

Answer 2

Example 1. The following two-equation system where x and y are dependent variables and t is the independent variable:

ole.gif

ole1.gif

or, equivalently,

2(D - 2)x + (D - 1)y = et

(D + 3)x + y = 0

where D = d/dt.

Example 2. The following three-equation system where x, y and z are dependent variables and t is the independent variable:

ole2.gif

ole3.gif

ole4.gif

or, equivalently,

Dx + (D + 1)y = 1

(D + 2)x - (D - 1)z = 1

(D + 1)y + (D + 2)z = 0

where D = d/dt.

Each equation in a system will be assumed to have constant coefficients and be of the general form

f(D)x + g(D)y + ....... + h(D)u = G(t)

where x, y, ...... , u are the dependent variables, t is the independent variable.

A system of n equations in the n dependent variables x, y, ..... , u and independent variable t will have a solution consisting of n functions

x = x(t)

y = y(t)

.............

.............

u = u(t)