Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
MAT244--2019F
»
MAT244--Lectures & Home Assignments
»
Chapter 4
»
4.2
« previous
next »
Print
Pages: [
1
]
Author
Topic: 4.2 (Read 979 times)
jeyara85
Jr. Member
Posts: 6
Karma: 0
4.2
«
on:
November 13, 2019, 10:42:22 PM »
I was wondering if we will be expected to find the characteristic equations of higher-order equations (3rd,4th, ..., nth), or will we be provided the characteristic equation in the exam.
Logged
david
Newbie
Posts: 3
Karma: 1
Re: 4.2
«
Reply #1 on:
November 14, 2019, 04:09:16 PM »
Finding the characteristic equation for higher order equations is very similar to the second order case.
If we have the differential equation $a_ny^{(n)} + a_{n-1}y^{(n-1)} .... + a_1y' + a_0y = 0$ then the characteristic equation is $a_nr^n + a_{n-1}r^{n-1} .... + a_1r + a_0 = 0$.
To find the roots, we can use the fact that the product of the roots must be $a_0$ to help guess the roots.
«
Last Edit: November 14, 2019, 04:13:43 PM by david
»
Logged
Victor Ivrii
Administrator
Elder Member
Posts: 2563
Karma: 0
Re: 4.2
«
Reply #2 on:
November 15, 2019, 02:42:45 PM »
Yes, because for equations given they could be found easily
Logged
ZeCheng Wu
Newbie
Posts: 1
Karma: 0
Re: 4.2
«
Reply #3 on:
November 17, 2019, 10:25:51 PM »
what if a
_{(n)}
is not a constant, like x^2 for example
Logged
david
Newbie
Posts: 3
Karma: 1
Re: 4.2
«
Reply #4 on:
November 18, 2019, 09:36:48 AM »
If any of the $a_i$'s are not constant, then we cannot use the method above. Non-constant coefficient differential equations are generally harder to solve. We discussed a few methods in class such as reduction of order or using the Wronskian, but both methods require already knowing one solution.
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
MAT244--2019F
»
MAT244--Lectures & Home Assignments
»
Chapter 4
»
4.2