Publisher Summary Differential equations occur in many physical problems. This chapter opens up with the explanation of some of these problems. To solve dy/dx =f(x,y) over the x range [a, b], the value is needed to know of y(a), which is called the initial value. Problems of this type are called initial value problems. With second-order differential equations two integration constants arise. For an initial value problem one needs to know the initial value of the two values of the dependent variables. Alternatively, the problem may be defined by specifying some conditions at one value of x and others at another value of x. Such problems are called boundary value problems. The chapter describes Euler's method to solve initial value problems. It also takes into account the Runge-Kutta method.