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

Rational, how can you identify if a certain number is rational or irrationa...

how can you identify if a certain number is rational or irrational?

Prove, Let Xn be a sequence of distinct real numbers. Defi ne E = {L : L is...

Let Xn be a sequence of distinct real numbers. Defi ne E = {L : L is a subsequential limit of Xn}. Prove E is closed.

Evolve a game to help children remember basic multiplication, Evolve a game...

Evolve a game to help children remember basic multiplication facts. In this section we have looked at ways of helping children absorb some simple multiplication facts. But what

Law of Cosines, The law of cosines can only be applied to acute triangles. ...

The law of cosines can only be applied to acute triangles. Is this true or false?

How many dollars did they raise the first two days, The freshman class is p...

The freshman class is participating in a fundraiser. Their target is to raise $5,000. After the first two days of the fundraiser, they have raised 32 percent of their goal. How man

Fractions, you need to cut the proper to cut 2''*4*8 long studs to the prop...

you need to cut the proper to cut 2''*4*8 long studs to the proper length to make a finished wall 8" in height underneath the studs there will be a double plate made up of two piec

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