Initial conditions and boundary conditions, Mathematics

Assignment Help:

Initial Conditions and Boundary Conditions

In many problems on integration, an initial condition (y = y0 when x = 0) or a boundary condition (y = y0 when x = x0 ) is given which uniquely determines the constant of integration. As a result of the unique determination of 'c', a specific curve can be singled out from a family of curves.

Example 

For the boundary condition, y = 15 when x = 2, the integral y =  ∫4dx is evaluated as follows:

y =  ∫4dx = 4x + c

Substituting, y = 15, when x = 2

15 = 4(2) + c or c  = 7

y = 4x + 7

Note that even though 'c' is specified, ∫4dx remains an indefinite integral because xn is unspecified. Thus, the integral 4x + 7 can assume an infinite number of possible values.


Related Discussions:- Initial conditions and boundary conditions

Permutations and combinations, number of ways that a mixed doubles tennis g...

number of ways that a mixed doubles tennis game can be arranged from 7 couples if no husband and wife play in the same game is??

Determine the approximate raw act score, Using the same mean and standard d...

Using the same mean and standard deviation as mean m = 20.1 and a standard deviation s = 5.8. Joe was informed that he scored at the 68 th percentile on the ACT, what was Joe's ap

Lorie, A bourbon that is 51 proof is 25.5% alcohol by volume while one that...

A bourbon that is 51 proof is 25.5% alcohol by volume while one that is 82 proof is 41% alcohol. How many liters of 51 proof bourbon must be mixed with 1.0 liter of 82 proof bourbo

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Find out the radius of convergence, Example: Find out the radius of conver...

Example: Find out the radius of convergence for the following power series. Solution : Therefore, in this case we have, a n = ((-3) n )/(n7 n+1 )   a n+1 = (

Free Assignment Test Online, Well, my uncle want me to tutor him in mathema...

Well, my uncle want me to tutor him in mathematics. But, the problem is I don''t know what he already knows about math. It for his Compass Test when he go back to school in the spr

Determine radicals in exponent form, Evaluate following.               ...

Evaluate following.                √16 and Solution To evaluate these first we will convert them to exponent form and then evaluate that since we already know how to

Calculate the mean, Calculate the mean, variance & standard deviation of th...

Calculate the mean, variance & standard deviation of the number of heads in a simultaneous toss of three coins.     SOLUTION:    Let X denotes the number of heads in a simu

Draw a common graph ( x - 2)2 /9+4(y + 2)2 =1, Graph     ( x - 2) 2 /9+4...

Graph     ( x - 2) 2 /9+4(y + 2) 2  = 1 Solution It is an ellipse. The standard form of the ellipse is                                                         ( x - h

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