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MAT244--2018F
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MAT244--Lectures & Home Assignments
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Linear differential equations
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Topic: Linear differential equations (Read 2015 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
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Last Edit: September 19, 2018, 02:31:15 AM by Victor Ivrii
»
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Wei Cui
Full Member
Posts: 16
Karma: 11
Re: linear differential equations
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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.
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Zifeng Zhu
Newbie
Posts: 2
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Re: linear differential equations
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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
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Tzu-Ching Yen
Full Member
Posts: 31
Karma: 22
Re: linear differential equations
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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.
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Last Edit: September 19, 2018, 02:31:53 AM by Victor Ivrii
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Victor Ivrii
Administrator
Elder Member
Posts: 2599
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Re: linear differential equations
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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.
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Last Edit: September 19, 2018, 06:26:09 AM by Victor Ivrii
»
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Toronto Math Forum
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MAT244--2018F
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MAT244--Lectures & Home Assignments
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Linear differential equations