Solve this differential equation:

#dy/dx-1=0#

#->dy/dx=1#

#->intdy=intdx#

Solving for the **general** solution gives:

#y=x+C#

Where #C# is the constant of integration. As #C# is yet undetermined and can take any (complex) value we call this the **general** solution. #C# might be #+2# or #-3# (though without further information there is no reason it can't be something like #1,4,pi,sqrt(10)# or #1+i#). These two values of #C# would give us:

#y=x+2# or #y=x-3#

In these cases #C# has been determined so these are **particular** solutions. In other words they are just **specific cases of the general solution**. The value of #C# can usually be worked out when given "initial" or "boundary" conditions.