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

Vector addition, Is it possible to add two vectors of unequal magnitude and...

Is it possible to add two vectors of unequal magnitude and get a resultant of zero?Please explain also. Ans) no it is not possible as .. if the magnitude is diffrent then they c

Transportation problem, 12. List the merits and limitations of using North ...

12. List the merits and limitations of using North West corner rule.

Differential equation.., 3.6Find the general solution of the differential e...

3.6Find the general solution of the differential equation Y" + 4y = Sec2 2x

Functions, find the domain of the function f(x) = (| sin inverse sin x | - ...

find the domain of the function f(x) = (| sin inverse sin x | - cos inverse cos x) ^ 1/2

Elli[ital paths of celestial bodies, Create a detailed diagram to describe ...

Create a detailed diagram to describe the equation of an ellipse in terms of it’s eccentricity and indicate how the foci and major and minor semi-axes are involved. Y

Numerical.analysis. , Please, I want to know and study "stability 0n predic...

Please, I want to know and study "stability 0n predictor -corrector method .My gmail is [email protected] heap and kind to me .Thanks for this.

Roman numerals, how to determine roman numerals to digits specially when it...

how to determine roman numerals to digits specially when it hundred thousands

Gravity, There is a list of the forces which will act on the object. Gr...

There is a list of the forces which will act on the object. Gravity, F g The force because of gravity will always act on the object of course. Such force is F g   = mg

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