A differential equation is defined as an equation which contains, in addition to independent variables and unknown functions, derivatives or differentials of the unknown functions. If the functions appearing in a differential equation depend on a single independent variable, the equation is called an ordinary differential equation. Whereas if partial derivatives of the functions with respect to certain of the independent variables appear in the equation, it is called a partial differential equation. The order of the differential equation is defined as the order n of the highest order derivative of the function that appears in the equation. This chapter discusses ordinary differential equations of the first order. A solution containing an arbitrary constant can be obtained in the general case of a first-order differential equation; such a solution is referred to as the general solution of the equation. On assigning different numerical values to the arbitrary constant, the various so-called particular solutions of the equation can be obtained.
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