Differential equation - variation of parameters, Mathematics

Assignment Help:

Variation of Parameters

Notice there the differential equation,

y′′ + q (t) y′ + r (t) y = g (t)

Suppose that y1(t) and y2(t) are a fundamental set of solutions for

y′′ + q (t ) y′ + r (t ) y = 0

888_Differential equation - Variation of Parameters1.png

Depending on the problem and the person, some will determine the formula easier to notice and use, whereas others will determine the process used to find the formula easier.  The illustrations in this section will be done using the formula.

 Before proceeding along with a couple of illustrations let's first address the issues including the constants of integration which will arise out of the integrals. Placing in the constants of integration will provide the following.

1823_Differential equation - Variation of Parameters.png

The last quantity in the parenthesis is nothing more than the complementary solution along with c1 = - c and c2 = k and we identify that if we plug this in the differential equation this will simplify out to zero as this is the solution to the homogeneous differential equation. Conversely, these terms add nothing to the particular solution and thus we will go ahead and suppose that c = 0 and k = 0 in all the illustrations.

One last note before we proceed along with illustrations.  Do not worry about that of your two solutions in the complementary solution is y1(t) and that one is  y2(t). This doesn't matter. You will finds out the same answer no matter that one you select to be y1(t) and which one you choose to be y2(t).


Related Discussions:- Differential equation - variation of parameters

Superimpose the three curves on the one axis, Submit solutions for all of t...

Submit solutions for all of the following questions. Remember to set out your answers showing all steps completely and explicitly justify your steps. 1. Provide, in no more than

Brahmaguptas problem, How to solve Brahmaguptas Problem? Explain Brahmagupt...

How to solve Brahmaguptas Problem? Explain Brahmaguptas Problem solving method?

Example of 3-d coordinate system, Example of 3-D Coordinate System Exam...

Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 .   Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co

A graph with a positive slope, A graph with a positive slope shows that the...

A graph with a positive slope shows that the variables depicted on the axes goes in the similar directions.

Trignometry, Sin3x ? Solution) THE FORMULA IS RIGHT ,SO sin3x=3sin...

Sin3x ? Solution) THE FORMULA IS RIGHT ,SO sin3x=3sinx-4sin 3 x

Project, elliptical path of celestial bodies

elliptical path of celestial bodies

How much money did carlie have after she had paid her friend, Carlie receiv...

Carlie received x dollars every hour she spent babysitting. She babysat a total of h hours. She then gave half of the money to a friend who had stopped through to help her. How muc

Word problems, if I read 6 hours of spring break how many minutes did ...

if I read 6 hours of spring break how many minutes did read

Math, 1+3+5+7+9+11+13+15+17+19

1+3+5+7+9+11+13+15+17+19

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