This lecture will improve your knowledge in differential equation lecture is by Lecturer AZEEM INAAM of SMI university.

1. DIFFERENTIAL EQUATION (MT-201) SYED AZEEM INAM
DIFFERENTIAL EQUATION (MT-201)
LECTURE #3
MORE ON FORMATION OF DIFFERENTIAL
EQUATIONS
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.

2. 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.