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

Shares and dividends, at what price a 6.25%rs 100 share be quoted when the ...

at what price a 6.25%rs 100 share be quoted when the money is worth 5%

How far apart are the two boats, Two boats leave the same port at the same ...

Two boats leave the same port at the same time. One travels at a constant speed of 30 km/hr at a bearing of 50° and the other on a bearing of 110° at a constant speed of 26 km/hr.

Multiplication of binomials, To understand the multiplication of binomials,...

To understand the multiplication of binomials, we should know what is meant by Distributive Law of Multiplication. Suppose that we are to multiply (a + b) and m. We

Mr F.D, how you divide 100 by 10 and then x by 10

how you divide 100 by 10 and then x by 10

Sums and differences of cubes and other odd powers, Sums and Differences of...

Sums and Differences of Cubes (and other odd powers)? You can factor a sum or difference of cubes using the formulas a 3 - b 3 = (a - b )(a 2 + ab + b 2 ) and a 3 + b 3 =

Duality., advanteges of duality

advanteges of duality

Find the average, The center of a national park is located at (0,0). A spec...

The center of a national park is located at (0,0). A special nature preserve is bounded by by straight lines connecting the points A at (3,2), B at (5,1), C at (8,4) and D at (6,5)

Calculate the fourier cosine series, The Fourier series expansion for the p...

The Fourier series expansion for the periodic function, f ( t ) = |sin  t | is defined in its fundamental interval. Taking π = 3.142, calculate the Fourier cosine series app

Simplification, if a+1/b=b+1/c=c+1/a then the value of abc is

if a+1/b=b+1/c=c+1/a then the value of abc is

Geometry help, One of two complementary angles is 80& of the other. What is...

One of two complementary angles is 80& of the other. What is the degree measure of the smaller angle?

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