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

Abstract algebra, Let D(subscript12) = ({x,y : x^2 = e ; y^6 = e ; xy =(...

Let D(subscript12) = ({x,y : x^2 = e ; y^6 = e ; xy =(y^-1) x}) a) Which of the following subsets are subgroups of D(subscript12) ? Justify your answer. i) {x,y,xy,y^2,y^3,e}

Solve the form x2 - bx + c, The form x2 - bx + c ? This tutorial will ...

The form x2 - bx + c ? This tutorial will help you factor quadratics that look something like this: x 2 -7x + 12 (No leading coefficient; negative middle coefficient; p

Sum and difference identities, Q. Sum and Difference Identities? Ans. ...

Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.

Example of set theory, Suggest me the solution: Consider the given unive...

Suggest me the solution: Consider the given universal set T and its subjects C, D and E T = {0, 2, 4, 6, 8, 10, 12} C = {4, 8,} D = {10, 2, 0} E = {0} Find out

Chp 8 Study, Center and Radius 1)(x+2)^2-(y-3)^2=4

Center and Radius 1)(x+2)^2-(y-3)^2=4

Math help until tuesday, I need help with pre algebra in 5th grade intermid...

I need help with pre algebra in 5th grade intermidate school math until Tuesday afternoon please

Multiplication of two like terms with opposite signs, The product of -7ab a...

The product of -7ab and +3ab is (-7 x 3) a 2  b 2  = -21a 2  b 2 . In other words, a term with minus sign when multiplied with a term having a positive sign, gives a product having

Minimizing the sum of two distances, The value of y that minimizes the sum ...

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

Strategy for series - sequences and series, Strategy for Series Now t...

Strategy for Series Now that we have got all of our tests out of the way it's time to think regarding to the organizing all of them into a general set of strategy to help us

Determine the tangent line to f ( x ) = 15 - 2x2 at x = 1, Determine the t...

Determine the tangent line to f ( x ) = 15 - 2x 2   at x = 1. Solution : We know from algebra that to determine the equation of a line we require either two points onto the li

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