# first example from class
dsolve({# diff is the differentiation function
        diff(y1(t), t) = 3*y1(t) + 4*y2(t),
        diff(y2(t), t) = 3*y1(t) + 2*y2(t),
        # initial conditions are additional equations
        y1(0) = 6, y2(0) = 1},
       {# must list unknowns as functions in t
        y1(t), y2(t)}
);

# harmonic motion example (second order)
dsolve({# diff(..., t$2) is the second derivative
        diff(y1(t), t$2) = -2*y1(t) +   y2(t),
        diff(y2(t), t$2) =    y1(t) - 2*y2(t),
        y1(0) = 0, y2(0) = 0,
        # D is the differentiation operator for use in initial cond
        D(y1)(0) = 2, D(y2)(0) = 2},
       {y1(t), y2(t)}
);