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

Left-handed limit, Left-handed limit We say provided we can mak...

Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m

Example of regression equation, Example of Regression Equation An inve...

Example of Regression Equation An investment company advertised the sale of pieces of land at different prices. The given table shows the pieces of land their costs and acreag

Math, a business is owned by three people.the first owns 1/12 of the busine...

a business is owned by three people.the first owns 1/12 of the business and the second owns 1/6 of the business. what fractional part of the business is owned by the third person

We know this equation a°=1.prove this?, we know that    A^m/A^m=1         ...

we know that    A^m/A^m=1                    so A^(m-m)=1                    so A^0=1.....

Produt promotion, What is the structure of produt promotion?

What is the structure of produt promotion?

Fractions, what Is the common denominator for 1/2 and 1/4

what Is the common denominator for 1/2 and 1/4

Evaluate the area of the shaded region, Evaluate the area of the shaded reg...

Evaluate the area of the shaded region in terms of π. a. 8 - 4π b. 16 - 4π c. 16 - 2π d. 2π- 16 b. The area of the shaded region is same to the area of the squa

Introducing counting, INTRODUCING COUNTING : From what you studied previou...

INTRODUCING COUNTING : From what you studied previous study, you know what it means to count. You would also agree that rote learning of number names does not always mean that the

Montel''s Theorem, In 5 pages, please try to prove Theorem 3 based on Monte...

In 5 pages, please try to prove Theorem 3 based on Montel''s Theorem. please use "Latex" Knuth Donald to write this paper. It is known that Theorem 3 on page 137 of the attached

Área de un rectangulo, calcula el área de la región sombreada de un rectáng...

calcula el área de la región sombreada de un rectángulo cuya base es 12.6 cm y su altura es 8.4

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