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

Find the distance between these two cities, Memphis, Tennessee, and New Orl...

Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35°N and New Orleans has latitude 30°N. Find the distance between these

Algebra, simplify mn+mp+nq+pq /n+p

simplify mn+mp+nq+pq /n+p

Probability, I have a question that hurts my head to work out. It is really...

I have a question that hurts my head to work out. It is really confusing for me. It sais " By the start of the 21st century, only 1 in 6 babies in America was born with blue eyes.

Photogrammetry, basic linear algebra concepts and calculations in photogram...

basic linear algebra concepts and calculations in photogrammetry

What is order of operations simplifying expressions, What is Order of Opera...

What is Order of Operations Simplifying Expressions? Kevin gives Don directions to his house: "Go left 3 blocks and then go right 2 blocks." Don wasn't paying close attention.

Solve following 4e1+3 x - 9e5-2 x = 0 logarithms, Solve following 4e 1+3 x...

Solve following 4e 1+3 x - 9e 5-2 x  = 0 . Solution Here the first step is to get one exponential on every side & then we'll divide both sides by one of them (that doesn'

Metric Units, How do I convert metric units?

How do I convert metric units?

Geometry, geometry fbw = 128 saf= 104 what is rfd

geometry fbw = 128 saf= 104 what is rfd

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