Here are a few basic Maple commands for dealing with differential equations.

We will look at Maple's abilities in more detail in our future Maple labs.

First, let's include the necessary Differential Equations tools.

>	with(DEtools);

We define a first order differential equation below...

>	deq := diff(y(x),x) = y(x)^2-1;

The following command plots the slope field the the differential equation defined above (called "deq").

The command tells Maple to display the slope field for values of x from -2 to 2 and y values from -2 to 2.

The list [[y(0)=0], etc.] tells Maple to plot integral curves through the points: (0,0), (0,1), and (0,-1).

>	DEplot(deq, y(x), x=-2..2,[[y(0)=0],[y(0)=1],[y(0)=-1]], y=-2..2);

Maple can solve a wide variety of differential equations. In fact, the equation defined above (i.e. "deq") can be

solved using Maple's "dsolve" routine.

>	dsolve(deq);

The solution shown above is the general solution. If we want to solve an initial value problem (IVP), we need

to specify an initial value (below we use the initial value "y(0) = -1"). This picks out one of the equilibrium solutions.

>	dsolve({deq,y(0)=-1},y(x));

Now lets find the solution through the origin.

>	dsolve({deq,y(0)=0},y(x));

>