Toronto Math Forum

MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Zifeng Zhu on September 18, 2018, 07:28:31 PM

Title: Linear differential equations
Post by: Zifeng Zhu on September 18, 2018, 07:28:31 PM
Is $xy' = 1$ a linear differential equation or not? Thanks
Title: Re: linear differential equations
Post by: Wei Cui 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.
Title: Re: linear differential equations
Post by: 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
Title: Re: linear differential equations
Post by: Tzu-Ching Yen 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.
Title: Re: linear differential equations
Post by: Victor Ivrii on September 19, 2018, 02:35:04 AM
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.