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

Example of negative number, Q. Example of negative number? If you take ...

Q. Example of negative number? If you take an elevator 8 stories  down , what would be the opposite of this? The opposite would be that you take the elevator 8 stories  up .

Area related to circles, railway tunnel of radius 3.5 m and angle aob =90 f...

railway tunnel of radius 3.5 m and angle aob =90 find height of the tunnel

Fractions, a boy is six months old his sister was given birth to three mont...

a boy is six months old his sister was given birth to three month after him. if their cousin is 0.33years old, arrange their ages in ascending order

Fundamentals of math, When there are 4 dots how many chords are they

When there are 4 dots how many chords are they

Simplify the boolean function, Simplify the Boolean function: F...

Simplify the Boolean function: F (w,x,y,z) = ∑ (0, 1, 2, 3, 4, 6, 8, 9, 12, 13, 14)  (8)  Ans:   f(w, x, y, z) = ∑(0, 1, 2, 3, 4, 6, 8, 9, 12, 13, 14) The above

What is the value of tan in terms of sin, What is the value of tan? in term...

What is the value of tan? in terms of sin?. Ans:    Tan ? = S i n ?/ C os ? Tan ? = S i n ? / √1 - S i n   2?

Intersection of perpendicular tangents of hyperbola., If angle between asym...

If angle between asymtotes of hyperbola x^2/a^2-y^2/b^=1 is 120 degrees and product of perpendicular drawn from foci upon its any tangent is 9. Then find the locus of point of inte

Differential equation, Verify Liouville''''s formula for y "-y" - y'''' + y...

Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1)

Explain expressions, Explain Expressions ? "One set of absolute value s...

Explain Expressions ? "One set of absolute value signs can only take the absolute value of one number." For example, For the absolute value of negative six plus three,

Compute projection scale factor, 1. A survey line on campus is measured to ...

1. A survey line on campus is measured to be 1000.00 ft long on horizontal ground. The elevation of the line is 700.00 feet and the geoid separation from ellipsoid to geoid is -110

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