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--2018F
»
MAT244--Lectures & Home Assignments
»
Linear differential equations
« previous
next »
Print
Pages: [
1
]
Author
Topic: Linear differential equations (Read 1915 times)
Zifeng Zhu
Newbie
Posts: 2
Karma: 0
Linear differential equations
«
on:
September 18, 2018, 07:28:31 PM »
Is $xy' = 1$ a linear differential equation or not? Thanks
«
Last Edit: September 19, 2018, 02:31:15 AM by Victor Ivrii
»
Logged
Wei Cui
Full Member
Posts: 16
Karma: 11
Re: linear differential equations
«
Reply #1 on:
September 18, 2018, 09:48:30 PM »
This equation is in the form of $a_0(x)y^{(n)} + a_1(x)y^{(n-1)} + ... + a_n(x)y = g(x)$. Therefore, $xy'=1$ is a linear equation.
Logged
Zifeng Zhu
Newbie
Posts: 2
Karma: 0
Re: linear differential equations
«
Reply #2 on:
September 18, 2018, 10:17:16 PM »
Thanks, cuz there is a website where the answer is no, so I asked to make sure
Logged
Tzu-Ching Yen
Full Member
Posts: 31
Karma: 22
Re: linear differential equations
«
Reply #3 on:
September 18, 2018, 10:23:08 PM »
Maybe in that website independent variable is $t$ and $x$, $y$ are the dependent variables. That could be why it's said to be nonlinear.
«
Last Edit: September 19, 2018, 02:31:53 AM by Victor Ivrii
»
Logged
Victor Ivrii
Administrator
Elder Member
Posts: 2599
Karma: 0
Re: linear differential equations
«
Reply #4 on:
September 19, 2018, 02:35:04 AM »
Quote from: Zifeng Zhu on September 18, 2018, 10:17:16 PM
Thanks, cuz there is a website where the answer is no, so I asked to make sure
References to "some website" do not cut. You need to provide link to it, so that we can learn if the website claims wrong or you just misunderstood what was written there.
«
Last Edit: September 19, 2018, 06:26:09 AM by Victor Ivrii
»
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
MAT244--2018F
»
MAT244--Lectures & Home Assignments
»
Linear differential equations