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

Coefficient of determination, It refers to the ratio of the explained varia...

It refers to the ratio of the explained variation to the total variation and is utilized to measure the strength of the linear relationship. The stronger the linear relationship th

Detemine multiplying a polynomial by a monomial, Detemine Multiplying a Pol...

Detemine Multiplying a Polynomial by a Monomial? To multiply a polynomial by a monomial, use the distributive property. Let's start by talking about ordinary numbers. Say th

What was the total cost of her order, Leslie ordered a slice of pizza for $...

Leslie ordered a slice of pizza for $1.95, a salad for $2.25, and a soda for $1.05. What was the total cost of her order? The cost of every item must be added together; $1.95 +

The quantity x + 6 is divided by negative four find number, Negative four i...

Negative four is multiplied through the quantity x + 8. If 6x is then added to this, the output is 2x + 32. What is the value of x? twice the quantity x + 6 is divided by negative

Sketch the feasible region, Sketch the feasible region for the following se...

Sketch the feasible region for the following set of constraints: 3y - 2x  ≥ 0 y + 8x  ≤  53 y - 2x  ≤  2 x  ≥ 3. Then find the maximum and minimum values of the objective

Standardizing a random variable, Standardizing a Random Variable       ...

Standardizing a Random Variable       If X is a random variable with E(X) = m and V(X) = s 2 , then Y = (X – m)/ s is a random variable with mean 0 and standard deviatio

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. Caculate the residual

What is the percent of increase heating oil, The price of heating oil rose ...

The price of heating oil rose from $1.10 per gallon to $1.43 per gallon. What is the percent of increase? The price of heating oil rose $0.33 ($1.43 - $1.10 = $0.33). To ?nd ou

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