How many solutions are there for differential equation, Mathematics

Assignment Help:

If a differential equation does have a solution how many solutions are there?

As we will see ultimately, this is possible for a differential equation to contain more than one solution. We would like to identify how many solutions there will be for a specified differential equation.

A sub-question here is as well. What types of conditions on a differential equation are required to acquire a single unique solution to the differential equation?

Both such question and the sub-question are more significant than you might realize. Assume that we derive a differential equation which will provide the temperature distribution in a bar of iron at any time t. If we resolve the differential equation and end up along with two or more completely different solutions we will have problems.  Look at the subsequent situation to see this.

If we subject 10 identical iron bars to identical conditions they must all exhibit similar temperature distribution. Thus only one of our solutions will be correct, but we will have no technique of knowing that one is the accurate solution.

This would be nice if, throughout the derivation of our differential equation, we could ensure that our assumptions would provide us a differential equation by solving, will yield a particular unique solution.

This question is generally termed as the uniqueness question in a differential equations course.


Related Discussions:- How many solutions are there for differential equation

Small samples-estimation of population mean , Estimation of population mean...

Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ±  tS x¯  x¯ = Sample mean S x¯ =  s/√n S = standard deviation

Ellpsoid, different kind of ellipsoid

different kind of ellipsoid

Determine the actual viewing area, Computer monitors are calculated by thei...

Computer monitors are calculated by their diagonals. If a monitor is advertised to be 19 in, Determine the actual viewing area, considerthe screen is square? (Round to the nearest

Step functions, Before going to solving differential equations we must see ...

Before going to solving differential equations we must see one more function. Without Laplace transforms this would be much more hard to solve differential equations which involve

surfaces z + |y| = 1, Describe and sketch the surfaces z + |y| = 1 and (x ...

Describe and sketch the surfaces z + |y| = 1 and (x   2) 2 y + z 2 = 0.

Progressions, The sum of the series 1+1/2+1/4,..is

The sum of the series 1+1/2+1/4,..is

Clique graph, Consider the clique graph below. a) How many subgraph...

Consider the clique graph below. a) How many subgraphs of G with 3 nodes are there?  b) How many of the subgraphs defined in part(a) are induced subgraphs?

Fractions, kim had 1/2 an orange. she gave Linda 1/4 of this. What fraction...

kim had 1/2 an orange. she gave Linda 1/4 of this. What fraction of the whole orange did Linda get?

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