Each of these categories can be divided into linear and nonlinear sub-categories. A differential equation is said to be linear if the dependent variable and all its derivatives appear to the power 1 and there are no products or functions of the dependent variable. Otherwise the differential equation is said to be nonlinear. Unfortunately that originate from

ways directly solvable or have nice closed form analytic solutions and therefore cannot be solved exactly. Instead, such solutions can only be approximated using numerical methods. As a result, the contents of this chapter will focus on the most popular and fundamental numerical methods for solving differential equations and illustrate how these methods may be coded in C#.