Hyperbolic Equation with Constant Coefficients:

The Charectric equations is;

           

and integration yields two families of straight lines

       

Notice that If A = 0 then the above equations is not valid. In this case we recall the above equations;

If we divide by as before we get;

         

Which is only linear and thus we get only one charectristic family. To overcome this difficulty we divide the above equations to get;

     

Which is quadratic now;

        

The transform is then,

    

Thus the Canonical form is just similar to the above equations.