PRESENTATION ON

Bernoulli’s Equation

BY

SYED AHMED ZAKIID:131-15-2169

ABOUT BERNOULLI

Bernoulli family consists of mathematicians.

Jacob Bernoulli Johann Bernoulli Daniel Bernoulli

Jacob and Johann’s Father is Nicolaus BernoulliAnd Daniel is the son of Johann’s Bernoulli.They all were from Switzerland.Jacob,Johann and Daniel were great mathematicians but there egotic nature made them away from each other.Their family bonding was not so good.

ABOUT JACOB BERNOULLI

Born in Basel, Switzerland 1654 and died in 1705He is a philosopher by academic degree but was a great mathematician by nature.

He was a great traveller also.

His differential equation first published in May 1690 in a paper named “Acta Eruditorum”

Leibnitz made the substitution method for Bernoulli's equation at 1696

EQUATION

This equation is true when n or n 1 but for any real number. If n=0 or n=1 we have linear equation.

Bernoulli’s differential equation is solved by leibnitz and that is

- - - - - - - - - - eqn 1

[ (1-n )xeqn 1]

EXAMPLE

The End