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

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

Determine the volume of the object, A rectangular container is 15 cm wide a...

A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the

Basic algebraic properties of real numbers, These can be expressed in...

These can be expressed in terms of two fundamental operations of addition and multiplication. If a, b and c are any three real numbers, then;     1.

Partial fraction decomposition - integration techniques, Partial Fraction D...

Partial Fraction Decomposition The procedure of taking a rational expression and splitting down it into simpler rational expressions which we can add or subtract to get the ori

What is terminology of quadratic functions, What is Terminology of Quadrati...

What is Terminology of Quadratic Functions ? The function in x given by: F(x) = ax 2 + bx + c, where a 0 is called a quadratic function. The graph of a quadratic function is

Define period, Q. Define Period, Amplitude and Phase Shift? Ans. P...

Q. Define Period, Amplitude and Phase Shift? Ans. Period, amplitude and phase shift are used when describing a sinusoidal curve The period of a function is the smallest

Find out the average temperature, Find out the average temperature: E...

Find out the average temperature: Example: Find out the average temperature if the subsequent values were recorded: 600°F, 596°F, 597°F, 603°F Solution: Step

Light take 5.3 × 10-6 seconds calculate standard notation, It takes light 5...

It takes light 5.3 × 10 -6 seconds to travel one mile. What is this time in standard notation? In order to convert this number to standard notation, multiply 5.3 through the f

Determine the permutation, There are 6 contestants for the post of chairman...

There are 6 contestants for the post of chairman secretary and treasurer. These positions can be filled by any of the 6. Find the possible no. of ways whether the 3 positions may b

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