Solve the given initial value problem, Programming Languages

Assignment Help:

Solve the following initial value problem

y(3) - 5y'' - 22y' + 56 y= 0;       y(0) = 1;           y'(0) = -2;         y''(0) = -4

Solution:

r3 - 5r2 - 22r + 56 = (r + 4)(r - 2)(r - 7) = 0

= r1 = -4, r2 = 4 and r3 = 7

Therefore we have three real distinct roots now and thus the general solution is,

y(t) = c1 e-4t + c2 ex2t + c3 ex7t

Differentiating a couple of times and applying the initial conditions provides the subsequent system of equations that we'll require solving in order to get the coefficients.

1 = y(0) = c1 + c2 + c3

-2 = y'(0) = - 4c1 + 2 c2 + 7 c3

-4 = y''(0) = 16 c1 + 4 c2 + 49 c3

After solving all these equations we get:

c1 = 14/33

c2 = 13/15

c3 = -(16/55)

Then the actual solution is,

 y(t) = (14/33) e-4t + (13/15) ex2t -(16/55)ex7t

Therefore, outside of requiring to solve a cubic polynomial that we left the details for you to verify and requiring to solve a system of 3 equations to get the coefficients that we also left for you to fill the details, the work currently is pretty much identical to the work we did in solving a 2nd order initial value problem.

Since the initial condition work is identical to work which we should be extremely familiar with to that point with the exception which it involved solving larger systems we're going to not bother with solving initial value problems for the rest of the examples. The basic point of this section is the new concepts involved in getting the general solution to the differential equation anyway and thus we'll concentrate on this for the remaining illustrations.

Also note that we'll not be demonstrating very much work in solving the characteristic polynomial. Here we are using computational aids and would encourage you to do similar here.  Solving these higher degree polynomials is simply too much work and would obscure the point of these illustrations.


Related Discussions:- Solve the given initial value problem

Fortran function for find and print out all prime number, Write a Fortran L...

Write a Fortran LOGICAL FUNCTION, called "is_prime", which determines if a given integer value is a prime number or not (A prime number is a natural number which has only two disti

Cookies management with perl, One of the main strengths of the Perl program...

One of the main strengths of the Perl programming language are its powerful text manipulation features. In this assignment, you will put them to  use for writing a Perl program tha

Assembly language, I need help with having a user input a year, and my prog...

I need help with having a user input a year, and my program to spit out what day of the week Christmas is on.... any helping hands on this?

No Linux Audible, Why no Audible support for Linux? Maybe they should use a...

Why no Audible support for Linux? Maybe they should use a browser interface?

Write a program to build bcd countdown timer, Many applications require ent...

Many applications require entering a number from a button and then the device counts that number down.  If it is a 2 digit number it can be stored in a single register.  If it is l

Pseudo code, I need help putting this into a flowchart constant c as Intege...

I need help putting this into a flowchart constant c as Integer = 3500 Constant CALORIESTOOUNCE as Integer = 219 Declare Sex as Character Declare Age as Integer Declare Weight as I

Find max and min no.from numbers passed through command line, Normal 0 ...

Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4

Django template, i''ve a problem with rendering a page with django template...

i''ve a problem with rendering a page with django templates

Write an implementation for the prime machine, You should use the BToolkit ...

You should use the BToolkit to produce the answers to the questions below. Where applicable, please use the machine names and identifier names suggested in the question to help me

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