Page 109 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes 2
 dy   dy 
a
(iii) x    y     0
 dx   dx 
2
2
   dy  2   3 2 d y   dy  2  3  d y  2
(iv)  1      2 or 1       2 
   dx    dx    dx     dx 
are examples of ordinary differential equations.

Did u know? The differential equations are solved and the solutions thus obtained are
interpreted in the context of the problem.

Self Assessment

Fill in the blanks:

1. A ................................ involves independent variables, dependent variables, their derivatives
and constants.
2. Ordinary differential equations are those, which involve only one ................................
variable.
3. The process of ................................ formulations of natural phenomena leads to a differential
equation.

State whether the following statements are true or false:
4. Ordinary differential equations involve more than one independent variable.

8.2 Classification of Differential Equation

A differential equation can be classified as ordinary or partial differential equation. A differential
equation involving a single independent variable and the derivatives with respect to it, is called
an ordinary differential equation.

Example: The equations (i), (ii), (iii) and (iv) given above are ordinary differential
equations.

Did u know? An ordinary differential equation contains total derivatives or total
differentials.
A differential equation involving two or more independent variables and the partial derivatives
with respect to them, is called a partial differential equation.

Example: the equations:

2 2
 v  v
(i) 2  2  0
x y

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