Actual solution to a differential equation, Mathematics

Assignment Help:

The actual solution is the specific solution to a differential equation which not only satisfies the differential equation, although also satisfies the specified initial conditions.

Illustration: What is the actual solution to the subsequent IVP?

2ty' + 4y = 3;    y(1) = -4

Solution: This is in fact easier to do than this might at first appear. From the earlier illustration we already identify that differential equations have all solutions are of the form:

y(t) = 3/4 + c/t2

All that we require to do is find out the value of c that will provide us the solution that we're after. To determine this all we require do is utilize our initial condition that are given as:

-4 = y(1) = 3/4 + c/12

c= -4 -3/4 = -19/4

Thus, the actual solution to the Initial Value Problem is:

y(t) = ¾ - 19/4t2

From this last illustration we can notice that once we have the general solution to a differential equation determining the actual solution is nothing more than applying the initial conditions and resolving for the constants which are in the general solution.


Related Discussions:- Actual solution to a differential equation

UNITARY METHOD, A group of 120 men had food for 200 days.After 5 days , 30 ...

A group of 120 men had food for 200 days.After 5 days , 30 men die of disease.How long will the remaining food last

Series solutions to differential equation, Before we find into finding seri...

Before we find into finding series solutions to differential equations we require determining when we can get series solutions to differential equations. Therefore, let's start wit

Managment Science, Classify models based on the degree of their abstraction...

Classify models based on the degree of their abstraction, and provide some examples of such models.

Interpretations of derivatives, Interpretations of derivatives. Exampl...

Interpretations of derivatives. Example:   Find out the equation of the tangent line to                                       x 2 + y 2   =9 at the point (2, √5 ) .

Minimum value of the function, How the property AM>or = GM used to get min...

How the property AM>or = GM used to get minimum value of the function......e,g for what condition of a and b does minimum value of a tan^2 x + b cot^2 x equals maximum value of a

Integerts, how do u add and subtract integers

how do u add and subtract integers

Phase plane, Before proceeding along with in fact solving systems of differ...

Before proceeding along with in fact solving systems of differential equations there's one topic which we require to take a look at. It is a topic that's not at all times taught in

Pair of linear equations in two variables, PAIR OF LINEAR EQUATIONS IN TWO ...

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES: Like  the  crest  of a  peacock so  is  mathematics  at the  head of all knowledge. Example At a certain time in a deer park, t

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