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

Assembly Language Programming, Complete the following program to move a val...

Complete the following program to move a value of 0xFFH to PORTB LIST p=18f4550 #include org 0x0000 movlw 0x00 _________ movlw 0xFF movwf PORTB end .

Write a program to use a robot to move, Write a program to use a robot to m...

Write a program to use a robot to move the stack of blocks from a source location to a target location, based. Movement of robot arms, picking and dropping, can be controlled usi

Capital gain calculator, This assignment is divided into two parts. The goa...

This assignment is divided into two parts. The goal is to write a Java program that calculates capital gain on a stock market, see Lab 7. When a share of common stock of some co

New features of visual studio 2008, New Features of Visual Studio 2008 1. L...

New Features of Visual Studio 2008 1. LINQ Support LINQ primarily is the structure of many conventional question employees that allow you to perform with information in a more user

Find the general solution, Example : Find the general solution to the subse...

Example : Find the general solution to the subsequent differential equation. x 2 y′′ - 7 xy′ + 16 y= 0   Solution First the roots of (3)  r (r -1) - 7r + 16= 0 r 2

Java help, I have a half done program that needs to be finished for a class...

I have a half done program that needs to be finished for a class by tomorrow night. The program will create a database and print out a menu ofoptions (already done). Ive already

Explain cascading style sheets, Question: (a) In JavaScript, the Windo...

Question: (a) In JavaScript, the Window Object is commonly used to request information from a user or to output some results. Give three ways how to create instances of the

Jsp help, what is the code to copy code on 1 jsp page to others

what is the code to copy code on 1 jsp page to others

Windows communication foundation, Windows Communication Foundation The Micr...

Windows Communication Foundation The Microsoft windows Interaction or communication foundation (or WCF), formerly known as "Indigo", is an application selection program (API) in th

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