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Chapter 8: Q5.23P (page 415)

Find the general solutions of the following equations and compare computer solutions.

D2+1D2-1y=0Hint:D2+1=(D+i)(D-i).

Short Answer

Expert verified

The general solution is y=c1e-ix+c2eix+c3ex+c4ex.

Step by step solution

01

Given information from question 

Given equation is D2+1D2-1y=0.

02

Differential equation

A differential equation is a formula that connects the derivatives of one or more unknown functions. Functions are used to represent physical quantities, derivatives are used to characterise their rates of change, and differential equations are used to define a relationship between them in applications.

03

Calculate the general solution

First expand the differential equation

(D+i)(D-i)(D+1)(D-1)y=0

It is found that the general solution for any differential that has an auxiliary equation with unequal roots is

y=c1eax+c2ebx+鈥�..+cneanx

In our cases it is a1=-i,a2=i,a3=-1,a2=1.Then, the general solution is,

y=c1e-ix+c2eix+c3ex+c4ex.

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Most popular questions from this chapter

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See all solutions

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