Determine an actual explicit solution, Mathematics

Assignment Help:

Determine an actual explicit solution to y′ = t/y; y(2) = -1.

Solution: We already identify by the previous illustration that an implicit solution to this IVP is y2 = t2 - 3.  To determine the explicit solution all we require to do is resolve for y(t).

y(t) = +√(t2 - 3)

Here, we've found a problem. Now there are two functions and we merely want one and actually only one will be correct! We can find out the correct function through reapplying the initial condition.  Only one of them will suit the initial condition.

In such case we can notice that the "-"solution will be the accurate one. The actual explicit solution is after that y(t) = - √(t2 - 3)

In such case we were capable to determine an explicit solution to the differential equation. It must be noted though that this will not for all time be possible to determine an explicit solution.

Also, notice that in such case we were only capable to find the explicit actual solution as we had the initial condition to assist us find out which of the two functions would be the accurate solution.

Now we've gotten most of the fundamental definitions out of the manner and thus we can move on other topics.


Related Discussions:- Determine an actual explicit solution

Assumptions and application of t distribution, Assumptions and Application ...

Assumptions and Application of T Distribution Assumptions of t distribution 1. The sample observations are random 2. Samples are drawn from general distribution 3.

Operation, What is a characteristic of operation

What is a characteristic of operation

Statistics Assignment, A. Design an investigation that details the followi...

A. Design an investigation that details the following six components:

Properties of reflection, explain under a reflection the image is laterally...

explain under a reflection the image is laterally inverted.

Ratio, There are only Chinese and Malay pupils in a hall.The ratio of the n...

There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys

What is the volume of the water required to fill the pool, A circular pool ...

A circular pool is filling along with water. Supposing the water level will be 4 ft deep and the diameter is 20 ft, what is the volume of the water required to fill the pool? (π =

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