Now, we provide some models to describe how the differential equations arise as models of real life problems.

**Formation of
Differential Equations**

** **

Now, we
provide some models to describe how the differential equations arise as models
of real life problems.

** **

According
to Newton’s second law of motion, 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.

Then,
the Newton’s second law is described by the differential equation

where *m* is the mass of the object, *h* is the height above the ground level.
This is the second order differential equation of the unknown height as a
function of time.

** **

The
population will increase whenever the offspring increase. For instance, let us
take rabbits as our population. More number of rabbits yield more number of
baby rabbits. As time increases the population of rabbits increases. If the
rate of growth of biomass *N* (*t*) of the population at time *t* is proportional to the biomass of the population,
then the differential equation governing the population is given by *dN/dt* = *rN*
, where *r* > 0* *is the growth rate.

** **

The rate
at which a disease is spread (*i.e.,*
the rate of increase of the number *N*
of people infected) in a fixed population *L*
is proportional to the product of the number of people infected and the number
of people not yet infected:

*dN/dL* = *kN* ( *L* −*N* ), *k* > 0 .

Tags : Mathematics , 12th Maths : UNIT 10 : Ordinary Differential Equations

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

12th Maths : UNIT 10 : Ordinary Differential Equations : Formation of Differential equations from Physical Situations | Mathematics

**Related Topics **

Privacy Policy, Terms and Conditions, DMCA Policy and Compliant

Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.