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

probability that the card is a 8 or an ace, A standard deck of cards conta...

A standard deck of cards contains 52 cards. One card is selected at random. Determine a)    The probability that the card is a 8 or an Ace? b)    The probability that the card is

Calculate the difference in payments of home mortgage loan, You have just r...

You have just renegotiated the interest rate of your home mortgage loan. (This is called rate modification.)  The original loan of $400,000 carries an interest rate is 6% has an or

Horizontal asymptote, The horizontal asymptote of (16x+7)(x^2-5)/(x^2+36).

The horizontal asymptote of (16x+7)(x^2-5)/(x^2+36).

Undamped - forced vibrations, We will firstly notice the undamped case. The...

We will firstly notice the undamped case. The differential equation under this case is, mu'' + ku  = F(t) It is just a non-homogeneous differential equation and we identify h

How would the society be strengthened, All things considered, in a sense of...

All things considered, in a sense of ethnicity (a sense of identification with and loyalty to one's group) good or bad? is it harmful or helpful? What would be lost if Americans lo

Dimensional analysis, Rachel had 3.25 quart of ice tea. her family drank 9 ...

Rachel had 3.25 quart of ice tea. her family drank 9 cups.How many cups are left

Calculate average speed of a train, Calculate average speed of a train: ...

Calculate average speed of a train: What is the average speed of a train which completes a 450-mile trip in 5 hours? Solution: Using Equation 15: V av = s/t V a

How many people should she expect not to show, Laura is planning her weddin...

Laura is planning her wedding. She expects 230 people to attend the wedding, but she has been told that around 5% typically don't show. About how many people should she expect not

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