The rate of change of y with respect to x is directly proportional to y

The rate of change of y with respect to x is directly proportional to the product of y2and x

The rate of change of y with respect to x is inversely proportional to y

The rate of change of y with respect to x is directly proportional to y2and inversely
proportional to x

A differential equation

If a differential equation is not expressible to polynomial equation form having the highest
order derivative as the leading term then

A nonlinear ordinary differential equation is

Newton’s second law of motion

Population Growth Model

General solution

Particular solution

Separation of variables was introduced initially by

The nucleus of an atom consists of combinations of protons and neutrons. Many of these
combinations of protons and neutrons are unstable, that is the atoms decay or transmute into the
atoms of another substance

A single differential equation can serve as

Newton’s law of cooling or warming

An equation in which some derivatives of the unknown function occur

the degree of the differential equation is not
defined.

One that is not linear

the
instantaneous acceleration a of an object with constant
mass m is related to the force F acting on the object by
the equation F = ma . In the case of a free fall, an object
is released from a height h t ( ) above the ground level

The population will increase whenever the offspring
increase.

The solution which contains as many arbitrary constants as the order of the differential
equation

If we give particular values to the arbitrary constants in the general solution of differential
equation, the resulting solution.

Leibniz and
later it was formulated by John Bernoulli in the year 1694.

Radioactive

A mathematical model for many different phenomena

the rate at which the
temperature of a body changes is proportional to the difference between the
temperature of the body and the temperature of the surrounding medium the so-called ambient
temperature