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

How to subtract fractions involving negative numbers, Q. How to Subtract fr...

Q. How to Subtract fractions involving negative numbers? Ans. This is the same as adding them, but just remember the rule that two negatives on the same fraction cancel ou

#title applications of vector and scalar , #question application of vector ...

#question application of vector and scalar in our daily life

Full asymptotic expansion , Consider the integral where the notatio...

Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri

Concrete operational stage, Concrete Operational Stage :  Piaget describes...

Concrete Operational Stage :  Piaget describes a five-year-old boy playing with a collection of pebbles. First, he laid them in a line and counted along the line from left to righ

Changing the base of the index, Changing The Base Of The Index For com...

Changing The Base Of The Index For comparison reasons if two series have different base years, this is difficult to compare them directly. In such cases, it is essential to ch

Find the value of a+b, If A, B are acute angles and sinA= cosB, then find t...

If A, B are acute angles and sinA= cosB, then find the value of A+B. Ans:    A + B = 90 o

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