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

Arthemetic progreession, ball are arranged in rows to form an equilateral t...

ball are arranged in rows to form an equilateral triangle .the firs row consists of one abll,the second of two balls,and so on.If 669 more balls are added,then all the balls canbe

How to calculate mode, Q. How to calculate Mode? The mode of a data set...

Q. How to calculate Mode? The mode of a data set is the value that is repeated most often in the data set. It has the highest frequency. There can be one, more than one, or n

Numbers, use the distributive law to write each multiplication in a differe...

use the distributive law to write each multiplication in a different way. the find the answer. 12x14 16x13 14x18 9x108 12x136 20x147

Matrices, how solve the inverse matrices using the matlab?

how solve the inverse matrices using the matlab?

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Solving trig equations with calculators part ii, Solving Trig Equations wit...

Solving Trig Equations with Calculators, Part II : Since this document is also being prepared for viewing on the web we split this section into two parts to keep the size of the

Dividing fractions by fractions with drawing.., how do I divide a fraction ...

how do I divide a fraction by a fraction by drawing a picture

Binary, how to divide a binaries

how to divide a binaries

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