# System of differential equations in Maple

I have problems entering a system of differential equations to Maple 13. Equations are:

$x' = -4x + 2y$
$y' = 5x - 4y$

Solve for $x = 0, y = 0$

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Have you seen this? – J. M. Apr 26 '11 at 18:27
@J. M. yes, the problem is, that examples contain y(t), x(t), but in my case it is x(y)=... y(x)=... – Kukmedis Apr 26 '11 at 18:42
...there is (supposed to be) an implied independent variable for your functions. So, something like $\frac{\mathrm d}{\mathrm dt}x(t)=-4x(t)+2y(t)$ and similarly for your second equation. – J. M. Apr 26 '11 at 18:45
When you write "solve for $x=0,y=0$", I presume you meant to give an initial condition, e.g. $x(0) = 0, y(0) = 0$? – Sam Lisi Apr 28 '11 at 0:07
@Sam It is as written in condition. Solve in dead point environment (x = 0, y = 0). I do not actually understand why there should be independent variable (maybe because I am not math student) – Kukmedis May 1 '11 at 20:09

I have two ways for solving this system of equations:

1)

sys := diff(x(t), t) = -4*x(t)+2*y(t), diff(y(t), t) = 5*x(t)-4*y(t):

f := {x(t), y(t)}:

dsolve({sys, x(0) = 0, y(0) = 0}, f);

2)

sys := [diff(x(t), t) = -4*x(t)+2*y(t), diff(y(t), t) = 5*x(t)-4*y(t)]:

p := dsolve(sys):

a1 := subs(x(t) = 0, t = 0, p[1]):

a2 := subs(y(t) = 0, t = 0, p[2]):

solve({a1, a2}, {_C1, _C2});

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