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

Solve for, a)Solve for ?, if tan5? = 1. Ans:    Tan 5? = 1        ⇒ ? ...

a)Solve for ?, if tan5? = 1. Ans:    Tan 5? = 1        ⇒ ? =45/5 ⇒ ?=9 o . b)Solve for ? if S i n ?/1 + C os ? + 1 +  C os ?/ S i n ? = 4 . Ans:  S i n ?/1 +

Limit comparison test - sequences and series, Limit Comparison Test Ass...

Limit Comparison Test Assume that we have two series ∑a n and ∑b n with a n , b n   ≥ 0 for all n. Determine, If c is positive (i.e. c > 0 ) and is finite (i.e. c

Give the introduction to amino acid and nucleotide metabolis, Give the Intr...

Give the Introduction to amino ACID and nucleotide metabolism ? Here, we studied about the chemistry of proteins and amino acids. We studied that the amino acids are used for p

Trigonometry, If a+b+c = 3a , then cotB/2 cotC/2 is equal to

If a+b+c = 3a , then cotB/2 cotC/2 is equal to

Cartesian product of sets, The Cartesian product (also called as the cross ...

The Cartesian product (also called as the cross product) of two sets A and B, shown by AΧB (in the similar order) is the set of all ordered pairs (x, y) such that x€A and y€B. What

Shares and dividend, how should i make my project on these topic?

how should i make my project on these topic?

Areas of a rectangle, a rectangular field with a path around it measures 1...

a rectangular field with a path around it measures 120m by 50m.if the path is 1m wide all around,(a)find the length of the outer edge of the path.(b)find the area of the path

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