In the practical work you will encounter examples which do not fit neatly into these categories. Higher order differential equations can be reduced to 1st order by appropriate choice of additional variables. The simplest such choice is to define new variables to represent all but the highest order derivative. Remember that there is no significance in the use of the letter in the above equations. We will have to employ an approximation.
All differential equations require boundary conditions.
For higher order equations the boundary conditions may be defined at different values of . We shall consider such problems later .