A differential equation is an equation with a function and one or more of its derivatives.

**Summary**

·
A differential equation is an equation
with a function and one or more of its derivatives.

(i.e) an equation with the function y = *f* (*x*)
and its derivatives , ... is called differential equation.

·
Order of the highest order derivative
present in the differential equation is the order of the differential equation.

·
Degree is the highest power of the highest order
derivative in the differential equation, after the equation has been cleared
from fractions and the radicals as for as the derivatives are concerned.

·
A function which satisfies the given differential
equation is called its solution. The solution which contains as many arbitrary
constants as the order of the differential equation is called a general
solution and the solution free from arbitrary constants is called particular
solution.

·
To form a differential equation from a given
function we differentiate the function successively as many times as the number
of arbitrary constants in the given function and then eliminate the arbitrary
constants.

·
In an equation it is possible to collect all the
terns of *x* and *dx* on one side and all the terms of *y* and *dy* on the other
side, then the variables are said to be separable. Thus the general form of
such an equation is *f* (*x*)*dx*
= *g* (*y*)*dy* (or) *f *(*x*)*dx
*+* g *(*y*)*dy
*=* *0* *By direct integration, we get the
solution.

·
A differential equation which can be expressed in
the form *dy/dx* = *f* ( *x*, *y*) or *dx/dy *=* g *(* x*,* y*)* *where* f *(* x*,* y*)* *and* g *(* x*,* y*)* *are homogeneous function of
degree zero* *is called a homogeneous
differential equation.

·
A differential equation of the form *dx/dy* + *Py* = *Q* where P and Q are constants or
functions of *x* only is called a first
order linear differential equation.

·
A general second order linear differential equation
with constant coefficients is of the form *a*
*d*^{2}*y/ dx*^{2} + *b* *dy/dx*
+ *cy* = *f* ( *x*)

Tags : Differential Equations , 12th Business Maths and Statistics : Chapter 4 : Differential Equations

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12th Business Maths and Statistics : Chapter 4 : Differential Equations : Summary | Differential Equations

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