DIFFERENTIAL EQUATION (MT-201) SYED AZEEM INAM

DIFFERENTIAL EQUATION (MT-201)

LECTURE #1

DIFFERENTIAL:

Sometimes we need a quick and simple estimate of the change in f(x) that results

from a given change in f(x) that results from a given change in x. Write y for f(x)

and suppose that the change in the independent variable x is the increment∆𝑥, so that

x changes from its original value of x to the new value x +∆𝑥. The actual change in

the value of y is the increment∆𝑦, computed by subtracting the old value of y from

its new value

∆𝑦 = f(x +∆𝑥) – f(x)

Now we compare the actual increment ∆𝑦 with the change that would occur in y if

it continued to change at the fixed rate f’(x) as x changes to x +∆𝑥. This hypothetical

change in y is called the differential

dy=f’(x) ∆𝑥

DIFFERENTIAL EQUATIONS:

An equation which involves independent variable, dependent variables and their

derivatives, is called a differential equations.

ORDINARY DIFFERENTIAL EQUATION:

If an equation which involves only one independent variable, one or more dependent

variables and their derivatives, is called and ordinary differential equation.

PARTIAL DIFFERENTIAL EQUATIONS:

If an equation which involves more than one independent variable, dependent

variable and its partial derivatives, is called a partial differential equation.

ORDER:

The order of a differential equation is the order of the highest differential coefficient

which occurs in the differential equation.

DIFFERENTIAL EQUATION (MT-201) SYED AZEEM INAM

DIFFERENTIAL EQUATION (MT-201)

DEGREE:

The degree of a differential equations is the power of the highest order differential

coefficient which occurs in the differential equations.

LINEAR AND NON-LINEAR DIFFERENTIAL EQUATIONS:

A differential equation is said to be linear differential equation of the dependent

variable and all its derivative are occurring in the first degree, otherwise the

differential equation is said to be non-linear. The differential equation is said to be

non-linear.

FORMATION OF DIFFERENTIAL EQUATIONS:

The differential equation can be obtained by differentiating an ordinary equation and

eliminating the arbitrary constants among them.