Definition :
1. An equation that involves independent and dependent variables and the derivatives of the dependent variables is called a differential equation
2. A differential equation is said to be ordinary, if the differential coefficients have reference to a single independent variable only and it is said to be partial if thee are two or more independent variables . We are concerned with ordinary differential equations only.
e.g. (d2y/dx2) +3(dy/dx)+2y=0 is an ordinary differential equation
(¶y/¶x)+( ¶x/¶y)+( ¶y/¶z)=0 ;( ¶2z/¶x2)+¶2/¶y2)=x2 + y are partial differential equation.
3. Finding the unknown function is called SOLVING OR INTEGRATING the differential equation. The solution of the differential equation is also called its PRIMITIVE, because the differential equation can be regarded as a relation derived from it.
4. ORDER AND DEGREE OF DIFFERENTIAL EQUATION :
The order of a differential equation is the order of the highest differential coefficient occuring in it.
The degree of a differential equation which is expressed or can be expressed as a polynomial in the derivatives is the degree of the highest order derivative occuring in it, after it has been expressed in a form free from radicals & fracrions so far as derivatives are concerned, thus the differential equation :
F(x,y) [dmy/dxm]p +Æ (x,y)[(dm-1(y)/dxm-1]q + ….= 0 is order m & degree p.
e. g.
(i) (d2y/dx2)=[y+(dy/dx)6]1/4
(ii) (dy/dx) +y =(1/(dy/dx))
(iii) e(d3y/dx3) -x(d2ydx2)+y=0
(iv) sin-1 (dy/dx) =x+yÞ(dy/dx)=sin(x+y)
