The first problem with the initial poster's attempt is the incorrect usage of D. It is possible to use diff, as suggested in the previous post, but here is how this equation should be entered with D:

ode:= D(D(y))(t)- u*(1-(y(t)^2))*D(y)(t) + y(t)=0;
ics:= y(0)=0.2, D(y)(0)=0;

Next, the second argument to dsolve needs to be the unknown function, in this case y(t):

dsolve({ode,ics},y(t));

Maple is unable to solve this equation exactly. But, it appears you are looking for a numeric solution. So, we use:

Y := dsolve({ode,ics},y(t),numeric);

This returns a Maple procedure that will return an approximate solution to the initial value problem. For example,

Y(0);
              [                                  d           ]
              [t = 0., y(t) = 0.20000000000000, --- y(t) = 0.]
              [                                  dt          ]

For any non-zero value of t, Maple needs a value for u to obtain the solution.

Y(1);
Error, (in Y) global 'u' must be assigned to a numeric value before obtaining a solution

Following this advise, you can assign a value to u (u := 3;). Or, you can avoid a global assignment by using subs:

subs(u=3,Y)(1);
   [                                       d                             ]
   [t = 1., y(t) = -0.114091806521692929, --- y(t) = -1.05459156309341574]
   [                                       dt                            ]

You will need to see the online help for numerical solutions to ODEs (?dsolve,numeric) for additional information on the different output you can obtain from dsolve and the ways to use this output.

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/
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