Principle of superposition, Mathematics

Assignment Help:

If y1 (t) and y2 (t) are two solutions to a linear, homogeneous differential equation thus it is y (t ) = c1 y1 (t ) + c2 y2 (t )   ........................(3)

Remember that we didn't comprise the restriction of constant coefficient or second order in this. It will work for any linear homogeneous differential equation.

If we further suppose second order and one other condition that we'll provide in a second we can go a step further.

If y1 (t) and y2 (t) are two solutions to a linear, second order homogeneous differential equation and they are "nice enough" so the general solution to the linear, second order differential equation is specified by (3).

So, just what do we mean by "nice enough"?  We'll hold off on that until a later section.  At this point you'll hopefully believe it when we say that specific functions are "nice enough".

Thus, if we now make the assumption as we are dealing along with a linear, second order differential equations, we now identify that (3) will be its general solution. The subsequent question which we can ask is how to get the constants c1 and c2. Because we have two constants it makes sense, confidently, which we will require two equations or conditions to get them.

One manner to do this is to identify the value of the solution at two distinct points or

y (t0) =  y0

 y (t1) = y1

 These are usually termed as boundary values and are not actually the focus of this course thus we won't be working along with them.

The other way to get the constants would be to identify the value of the solution and its derivative at an exacting point.  Or,

 y (t0) =  y0

 y′ (t0) = y0

These are the two conditions which we'll be using here. When with the first order differential equations these will be termed as initial conditions.


Related Discussions:- Principle of superposition

Find out the mean time, 1 . The probability that a couple will have a child...

1 . The probability that a couple will have a child with black hair is 0.6. If this couple has 7 children what is (a) the probability that exactly 3 of these children have bl

Perimeter of trinagle, what is the perimeter of a triangele with the sides ...

what is the perimeter of a triangele with the sides of 32 in /22 in/20 in/

Which mathematical property did marty use to get similar ans, Marty used th...

Marty used the subsequent mathematical statement to show he could change an expression and still get the similar answer on both sides: 10 × (6 × 5) = (10 × 6) × 5 Which mathematica

Right- and left-handed limits , Right- and left-handed limits : Next, let'...

Right- and left-handed limits : Next, let's see precise definitions for the right- & left-handed limits. Definition   For the right-hand limit we say that, if for eve

Take home test, what is 36 percent as a fraction in simplest form

what is 36 percent as a fraction in simplest form

How far is balloon from the shore, Steve Fossett is going the shores of Aus...

Steve Fossett is going the shores of Australia on the ?rst successful solo hot air balloon ride around the world. His balloon, the Bud Light Spirit of Freedom, is being escorted

Triangle inequalities, poa is a straight line in circle,wher o is center of...

poa is a straight line in circle,wher o is center of circle,b is any pointjoined with p.prove that pa>pb

Compute the break-even quantities, The revenue and cost functions for produ...

The revenue and cost functions for producing and selling quantity x for a certain production facility are given below. R(x) = 16x - x 2 C(x) = 20 + 4x a)  Determine the p

Determine all possible solutions to ivp, Determine all possible solutions t...

Determine all possible solutions to the subsequent IVP. y' = y ? y(0) = 0 Solution : First, see that this differential equation does NOT satisfy the conditions of the th

Heat loss in cylindrical pipe, which physics law is used to describe heat l...

which physics law is used to describe heat loss in cylindrical pipe

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