Author Topic: Linear differential equations  (Read 1430 times)

Zifeng Zhu

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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 »

Wei Cui

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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.

Zifeng Zhu

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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

Tzu-Ching Yen

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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 »