odrinary diffential equation
General definition [ edit ] Given F , a function of x , y , and derivatives of y . Then an equation of the form � ( � , � , � ′ , … , � ( � − 1 ) ) = � ( � ) is called an explicit ordinary differential equation of order n . [8] [9] More generally, an implicit ordinary differential equation of order n takes the form: [10] � ( � , � , � ′ , � ″ , … , � ( � ) ) = 0 There are further classifications: Autonomous A differential equation not depending on x is called autonomous . Linear A differential equation is said to be linear if F can be written as a linear combination of the derivatives of y : � ( � ) = ∑ � = 0 � − 1 � � ( � ) � ( � ) + � ( � ) where a i ( x ) and r ( x ) are continuous functions of x . [8] [11] [12] The function r ( x ) is called the source term , leading to two further important classifi...