Actual solution to a differential equation, Mathematics

Assignment Help:

The actual solution is the specific solution to a differential equation which not only satisfies the differential equation, although also satisfies the specified initial conditions.

Illustration: What is the actual solution to the subsequent IVP?

2ty' + 4y = 3;    y(1) = -4

Solution: This is in fact easier to do than this might at first appear. From the earlier illustration we already identify that differential equations have all solutions are of the form:

y(t) = 3/4 + c/t2

All that we require to do is find out the value of c that will provide us the solution that we're after. To determine this all we require do is utilize our initial condition that are given as:

-4 = y(1) = 3/4 + c/12

c= -4 -3/4 = -19/4

Thus, the actual solution to the Initial Value Problem is:

y(t) = ¾ - 19/4t2

From this last illustration we can notice that once we have the general solution to a differential equation determining the actual solution is nothing more than applying the initial conditions and resolving for the constants which are in the general solution.


Related Discussions:- Actual solution to a differential equation

Emi, calculation of emi %

calculation of emi %

Erp for a company, recomendation to a company to implement ERP to succeed

recomendation to a company to implement ERP to succeed

Example of the invisible effort, Imagine a time in history when the number ...

Imagine a time in history when the number system had not yet evolved a farmer needed to keep track of his cattle. What would he do to figure out whether his entire rattle returned

Trigonometry, If a+b+c = 3a , then cotB/2 cotC/2 is equal to

If a+b+c = 3a , then cotB/2 cotC/2 is equal to

Pre-algebra, How do you solve a table to get the function rule?

How do you solve a table to get the function rule?

Surface area with polar coordinates, Surface Area with Polar Coordinates ...

Surface Area with Polar Coordinates We will be searching for at surface area in polar coordinates in this part.  Note though that all we're going to do is illustrate the formu

Ordinary and partial differential equations, A differential equation is ter...

A differential equation is termed as an ordinary differential equation, abbreviated through odes, if this has ordinary derivatives in it. Similarly, a differential equation is term

Which state sold corsica to france in 1768, By which of those ancient civil...

By which of those ancient civilizations was Machu Pichu built? The Aztecs The Egyptians The Mayas The Incas Which state sold Corsica to France in 1768? - Not answered Genoa Veni

Unitary methods, john walked to school at an average speed of 3 miles/hr a...

john walked to school at an average speed of 3 miles/hr and jogged back along the same route at 5miles/hr. if his total time was 1 hour, what was the total number of miles in the

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