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

Graphs, the value of y for which x=-1.5

the value of y for which x=-1.5

Solve following x - x e 5 x + 2 = 0 logarithms, Solve following  x - x  ...

Solve following  x - x  e 5 x + 2   = 0 . Solution : The primary step is to factor an x out of both terms. DO NOT DIVIDE AN x FROM BOTH TERMS!!!! Note as well that it i

Compute standard and variance deviation, A firm is manufacturing 45,000 uni...

A firm is manufacturing 45,000 units of nuts. The probability of having a defective nut is 0.15 Compute the given i. The expected no. of defective nuts ii. The standard an

What was the original price of the frying pan, Cory purchased a frying pan ...

Cory purchased a frying pan which was on sale for 30% off. She saved $3.75 along with the sale. What was the original price of the frying pan? Use a proportion to ?nd out the o

Inequalality, the low temperature in onw city was -4degrees Fahrenheit. The...

the low temperature in onw city was -4degrees Fahrenheit. The low temperature in another city was 8degrees Fahrenheit. what is an inequality to compare those temperatures

Find where the breakdown occurred and his original speed, A cyclist, after ...

A cyclist, after riding a certain distance, stopped for half an hour to repair his bicycle, after which he completes the whole journey of 30km at half speed in 5 hours.  If the bre

Trig substitutions - integration techniques, Trig Substitutions - Integrati...

Trig Substitutions - Integration techniques As we have completed in the last couple of sections, now let's start off with a couple of integrals that we should previously be

Determine the distance, Two planes leave the airport at the similar time. M...

Two planes leave the airport at the similar time. Minutes later, plane A is 70 miles due north of the airport and plane B is 168 miles due east of the airport. Determine the distan

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