ODE - Seconed Semester - LEC 1

An equation that consists of derivatives is called a differential equation. Differential equations have applications in all areas of science and engineering. Mathematical formulation of most of the physical and engineering problems leads to differential equations. So, it is important for engineers and scientists to know how to set up differential equations and solve them.

Differential equations are of two types
(A) ordinary differential equations (ODE)
(B) partial differential equations (PDE)

An ordinary differential equation is that in which all the derivatives are with respect to a single independent variable. Examples of ordinary differential equations include

Ordinary differential equations are classified in terms of order and degree. Order of an ordinary differential equation is the same as the highest derivative and the degree of an ordinary differential equation is the power of highest derivative.


An engineer’s approach to differential equations is different from a mathematician. While, the latter is interested in the mathematical solution, an engineer should be able to interpret the result physically. So, an engineer’s approach can be divided into three phases:
a) formulation of a differential equation from a given physical situation,
b) solving the differential equation and evaluating the constants, using given conditions, and
c) interpreting the results physically for implementation.