Theorem on intervals of validity, Mathematics

Assignment Help:

Theorem

Consider the subsequent IVP.

y′ =  p (t ) y = g (t )

 y (t0)= y0

If p(t) and g(t) are continuous functions upon an open interval a < t  < b and the interval includes to, after that there is a unique solution to the IVP on such interval.

 Therefore, just what does this theorem tell us? Initially, it tells us that for nice adequate linear first order differential equations solutions are guaranteed to exist and more significantly the solution will be particular. We may not be capable to get the solution, but do identify that it exists and which there will only be one of them. It is the very significant aspect of this theorem. Identifying that a differential equation has a unique solution is probably more significant than actually having the solution itself!

Subsequently, if the interval in the theorem is the largest possible interval on that p(t) and g(t) are continuous so the interval is the interval of validity for the solution. This means that for linear first order differential equations, we won't want to actually solve the differential equation in order to get the interval of validity. See that the interval of validity will based only partially on the initial condition. The interval should hold to, but the value of yo, has no consequence on the interval of validity.


Related Discussions:- Theorem on intervals of validity

Exponential and geometric model, Exponential and Geometric Model Expo...

Exponential and Geometric Model Exponential model  y = ab x Take log of both sides log y = log a + log b x log y = log a + xlog b Assume log y = Y and log a

Pair of linear equations in two variables, a lending library has a fixed ch...

a lending library has a fixed charge for the first three days and an additional charge for each day thereafter. sam paid Rs 27 for a bookkept for 7 days while jaan paid Rs 21 for t

Word problem, Twins Olivia and Chelsea and their friend Rylee were celebrat...

Twins Olivia and Chelsea and their friend Rylee were celebrating their fourteenth birthdays with a party at the beach. The first fun activity was water games. As Nicole arrived, sh

Joey participated-a-thon how many hours did joey team dance, Joey participa...

Joey participated within a dance-a-thon. His team begin dancing at on Friday 10 A.M. and stopped at 6 P.M. on Saturday. How many hours did Joey's team dance? From 10 A.M. Frida

Basic algebraic properties of real numbers, These can be expressed in...

These can be expressed in terms of two fundamental operations of addition and multiplication. If a, b and c are any three real numbers, then;     1.

Fiancial project, With your current loan, explain how much additional money...

With your current loan, explain how much additional money you would need to add to your monthly payment to pay off your loan in 20 years instead of 25. Decide whether or not it wou

Matrix, how to solve for x

how to solve for x

Find out the mean time, 1 . The probability that a couple will have a child...

1 . The probability that a couple will have a child with black hair is 0.6. If this couple has 7 children what is (a) the probability that exactly 3 of these children have bl

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