Solving Equations

There are many Maple functions for solving systems of different kinds of
equations.  The simplest and most commonly used of these is solve, which
solves algebraic systems of equations:

> # Solve a single equation with one unknown and one solution:
> solve(exp(x) = 1);
0
> # Solve a single equation with a constant, an unknown, and two solutions:
> solve(x^2 = a, x);
 1/2     1/2
a   , - a
> # An expression like "x+y" is implicitely assumed to be equal to 0.
> # Solve a system of equations simultaneously:
> solve( {x+y, x*y=b}, {x,y} );
            1/2           1/2             1/2             1/2
{y = - (- b)   , x = (- b)   }, {y = (- b)   , x = - (- b)   }

The function for solving differential equations is dsolve.  For full
details on using it, see help('dsolve').  Here is a simple example:

> deq := diff(y(x),x) + y = 0; 
       /  d      \
deq := |---- y(x)| + y = 0
       \ dx      /
>  dsolve(deq, y(x));
y(x) = exp(- x) _C1

As the various solve functions need to specify solution constants, they
generate names like "_C1", "_C2", etc.