NCERT Book Class 12 Maths Chapter 9 Differential Equations

300 MATHEMATICS

Chapter 9
DIFFERENTIAL EQUATIONS

v He who seeks for methods without having a definite problem in mind
seeks for the most part in vain. – D. HILBERT v

9.1 Introduction
In Class XI and in Chapter 5 of the present book, we
discussed how to differentiate a given function f with respect
to an independent variable, i.e., how to find f ′(x) for a given
function f at each x in its domain of definition. Further, in
the chapter on Integral Calculus, we discussed how to find
a function f whose derivative is the function g, which may
also be formulated as follows:
For a given function g, find a function f such that
dy
= g (x), where y = f (x) ... (1)
dx
An equation of the form (1) is known as a differential Henri Poincare
equation. A formal definition will be given later. (1854-1912 )

These equations arise in a variety of applications, may it be in Physics, Chemistry,
Biology, Anthropology, Geology, Economics etc. Hence, an indepth study of differential
equations has assumed prime importance in all modern scientific investigations.
In this chapter, we will study some basic concepts related to differential equation,
general and particular solutions of a differential equation, formation of differential
equations, some methods to solve a first order - first degree differential equation and
some applications of differential equations in different areas.
9.2 Basic Concepts
We are already familiar with the equations of the type:
x2 – 3x + 3 = 0 ... (1)
sin x + cos x = 0 ... (2)
x+y=7 ... (3)