You can solve single equations and systems of linear and non-linear equations exactly with the solve command. For approximate solutions, use the fsolve command. For ordinary differential equations use the dsolve command. And for recurrence equations use the rsolve command. These commands have the following syntax.
For example, to solve the equation for
> solve( x^3-6*x=5, x );
1/2 1/2
-1, 1/2 + 1/2 21 , 1/2 - 1/2 21
To solve the ODE given initial conditions
and
> dsolve({y(x)+diff(y(x),x$2)=exp(x), y(0)=1, D(y)(0)=0}, y(x));
y(x) = 1/2 exp(x) - 1/2 sin(x) + 1/2 cos(x)