## Sets of first order differential equations

You can also enter a set of differential equations. In this case you need to indicate what the output variables are. For example,
```>> [x1,x2] = dsolve('Dx1=5*x1-2*x2','Dx2=7*x1-4*x2')

x1 =
-2/5*C1*exp(-2*t)+7/5*C1*exp(3*t)-2/5*C2*exp(3*t)+2/5*C2*exp(-2*t)
x2 =
7/5*C1*exp(3*t)-7/5*C1*exp(-2*t)+7/5*C2*exp(-2*t)-2/5*C2*exp(3*t)
```
gives the general solution of equation (5.2). Note that this general solution depends on arbitrary constants and . If you want to specify initial conditions, you can do this in the following way:
```>> [x1,x2] = dsolve('Dx1=5*x1-2*x2','Dx2=7*x1-4*x2','x1(0)=0','x2(0)=5')

x1 =
2*exp(-2*t)-2*exp(3*t)
x2 =
-2*exp(3*t)+7*exp(-2*t)
```
If you want to plot the functions and , you can do this with the commands `ezplot(x1)` and `ezplot(x2)`. If you want to plot the state [ , ] in the phase plane, you first need to calculate and for a range of values of . For example:
```>> t = [0:0.1:1];
>> X = subs(x1,t);
>> Y = subs(x2,t);
>> plot(X,Y)
```

Esteur 2010-03-22