CHAPTER XX 



164. A differential equation is an equation connecting x, y and 

 a differential coefficient, or differential coefficients of y with 

 respect to x. The order of a differential equation is the order of 

 the highest differential coefficient occurring in it. Thus an equa- 



dii 



tion of the first order is one containing -p, one of the second order 



fU 



d?ii 



would contain -j-4, while an equation of the nth order would con- 

 oar 



A differential equation can be obtained by the elimination of 

 the constants in a law connecting x and y, and the following ex- 

 amples will show how differential equations can be obtained in 

 this way. 



(a) If xy = a 

 Then a-g+tf-O 



(b) If x 2 +y 2 = a 2 



Then 2x + 2y / = 



ax 



dy 

 or a+yjg-0 



(c) If t/ = or + 6,r 2 



20 



Now x ~ = ax + Zbx 2 



dx 



Hence x -^ - y = bx 2 



dx 



and -- 



dx 2 dx 



319 



