IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

spideyunlimited

d^3y/dx^3 + d^2y/dx^2 - 2dy/dx = 0

d^3y/dx^3 + d^2y/dx^2 = 2dy/dx

[ d^3y/dx^3 + d^2y/dx^2 ] / 2 = dy/dx

now LHS is average of 2 terms...
if RHS is the average of the terms in the numerator of LHS, then it implies from it that :
Either ...
1) 1 term is larger than and 1 term is smaller than RHS term by same amount.
or 2) both terms are the same in value.

(Example : (3 + 5) / 2 = 4
or (4 + 4) / 2 = 4
)

But (1) cannot b true!!!
since derivative of an expression cannot be larger in value than the expression itself.. it is always less than equal to.

Hence we are left with (2)
so .... d^3y/dx^3 = d^2y/dx^2 = dy/dx
so the value remains the same no matter wat order derivative it is.
And only one such expression i know :
e^x
:)

Ask & Discuss Questions with Community & Experts