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

Probability, TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 N...

TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 NOON.  THE FIRST ONE TOARRIVE WAITS FOR 20 MIN AND THEN LEAVE. IF THE TIME OF THIR ARRIVAL BE INDEPENDET AND AT RNDOM,T

Properties of logarithms, Properties of Logarithms 1. log a x...

Properties of Logarithms 1. log a xy = log a x + log a y 2.  = log a x - log a y 3. log a x n   = n log

DECIMALS, the mass of a container is 5.81kg when full with sugar .the mass ...

the mass of a container is 5.81kg when full with sugar .the mass of container is 3.8kg when 3/8 of the sugar is removed.what is the mass of empty container

Applying quadratics math question, A boat tour company charges $11 for a ha...

A boat tour company charges $11 for a harbour tour and averages 450 passengers on Saturdays. Over the past few months, the company has been experimenting with the price of a tour a

Law of cosines - vector, Theorem a → • b → = ||a → || ||b → || cos• ...

Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha

Lim x, Q. lim x tends to 0 (5 tanx sinx upon x square) here ( ) this bracke...

Q. lim x tends to 0 (5 tanx sinx upon x square) here ( ) this bracket indicates greatest integer function Ans: You can calculate the limit of this function using basic concept of

Quantitative method, Year 1 2 3 4 ...

Year 1 2 3 4 5 6 7 8 9 10 Corn revenue 40 44 46

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