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Solving a Linear System
Math 308
In this example, we see how to solve a linear system of the form
x'=Ax.
Suppose
=
A
±
²
³
´
µ
1

2
4

5
and we want to solve
x
' = A
x,
where
x
=
±
²
³
´
µ
( )
x
t
( )
y
t
The differential equation written in matrix form above is really two first order equations:
x'(t) = x(t)  2y(t)
y'(t) = 4x(t)  5y(t)
We define the problem in Maple by entering these equations individually:
>
eq1 := diff(x(t),t) = x(t)2*y(t);
:=
eq1
=
∂
∂
t
( )
x
t

( )
x
t
2 ( )
y
t
>
eq2 := diff(y(t),t) = 4*x(t)5*y(t);
:=
eq2
=
∂
∂
t
( )
y
t

4 ( )
x
t
5 ( )
y
t
We can use the
dsolve
function to solve the system.
As usual, the first argument to
dsolve
is the
problem to be solved, and the second argument holds the functions to be found.
In this case, the
problem is a system, so we put both equations in brackets.
Also, there are two functions to be found,
so we also put them in brackets.
>
sol := dsolve([eq1,eq2],[x(t),y(t)]);
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 Spring '08
 McAllister
 Math

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