Theorem of continuous functions, Mathematics

Assignment Help:

Consider the subsequent IVP.

y' = f(t,y) ,        y(t0) = y0

If f(t,y) and ∂f/∂y are continuous functions in several rectangle a < t < b, g < y  < d, containing the point  (to, yo) then there is a unique solution to the IVP in some interval to - h < t < to + h which is included in a < t < b.

That's it.  Unlike the first theorem, this one cannot really be used to find an interval of validity. Thus, we will know that a unique solution exists if the conditions of the theorem are met, but we will in fact need the solution in order to find out its interval of validity.  Remember as well that for non-linear differential equations it emerges that the value of y0 may influence the interval of validity.

Here is an illustration of the problems that can happen when the conditions of this theorem are not met.


Related Discussions:- Theorem of continuous functions

Jordan needs help, carlie is now fivetimes as old as henry. in nine years ...

carlie is now fivetimes as old as henry. in nine years her age will be twice henry''s age then. how old is carly now

TRIGONOMETRY, EXPLAIN ME ABOUT ITS FUNCTIONS.

EXPLAIN ME ABOUT ITS FUNCTIONS.

Regression, regression line drawn as Y=C+1075x, when x was 2, and y was 239...

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Algebra, 2x+2y=10 and 3y+4x=9

2x+2y=10 and 3y+4x=9

Need some clarity?, THE % PARTICIPATION Feature in a major medical expense ...

THE % PARTICIPATION Feature in a major medical expense policy is 75% with a $100 deductible. how much of a $2,000 bill is the insured responsible for paying?

Unit circle, Unit circle A circle centered at the origin with radius 1 ...

Unit circle A circle centered at the origin with radius 1 (i.e. this circle) is called as unit circle.  The unit circle is very useful in Trigonometry. (b) x 2 + ( y - 3) 2

Frobenius number, Wht is Frobenius Number? Start discussion and problems so...

Wht is Frobenius Number? Start discussion and problems solving in Frobenius Number.

Find the interval of validity for the solution, Solve the subsequent IVP an...

Solve the subsequent IVP and find the interval of validity for the solution xyy' + 4x 2 + y 2 = 0,       y(2) = -7,          x > 0 Solution: Let's first divide on both

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