Theorem of continuous functions, Mathematics

Assignment Help:

Consider the subsequent IVP.

y' = f(t,y) ,        y(t0) = y0

If f(t,y) and ∂f/∂y are continuous functions in several rectangle a < t < b, g < y  < d, containing the point  (to, yo) then there is a unique solution to the IVP in some interval to - h < t < to + h which is included in a < t < b.

That's it.  Unlike the first theorem, this one cannot really be used to find an interval of validity. Thus, we will know that a unique solution exists if the conditions of the theorem are met, but we will in fact need the solution in order to find out its interval of validity.  Remember as well that for non-linear differential equations it emerges that the value of y0 may influence the interval of validity.

Here is an illustration of the problems that can happen when the conditions of this theorem are not met.


Related Discussions:- Theorem of continuous functions

Example of identify the pre-requisites, Ravi is a teacher of Class 4 in a m...

Ravi is a teacher of Class 4 in a municipal school in Delhi. When the new school year started, he opened the textbook and started teaching the children how to write 4-digit numbers

Circles, assignment on theorems on circle for class 9

assignment on theorems on circle for class 9

Trigonometry, important trigonometric formulas for class 10th CBSC board

important trigonometric formulas for class 10th CBSC board

Operation research, discuss the sequencing decision problem for n jobs on t...

discuss the sequencing decision problem for n jobs on two and three machines

Shares and dividents., how much money will required to buy 200,rupees 25 sh...

how much money will required to buy 200,rupees 25 shares at premium of rupees 2

How much did donald earn in commissions last month, Donald sold $5,250 wort...

Donald sold $5,250 worth of latest insurance policies last month. If he receives a commission of 7% on new policies, how much did Donald earn in commissions last month? To ?nd

Definite integration-mathematics, Definite integration It involve integ...

Definite integration It involve integration among specified limits, say a and b The integral    is a definite integral whether the limits of integration are as: a and b

Determine y inverse for x2 + y 4 = 10, Determine  y′′  for           ...

Determine  y′′  for                                x 2 + y 4   = 10 Solution: We know that to get the second derivative we required the first derivative and to get that w

Algebra, how to solve algebra

how to solve algebra

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd