Linear differential equations

[Zifeng Zhu]

Is $xy' = 1$ a linear differential equation or not? Thanks

[Wei Cui]

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]

Thanks, cuz there is a website where the answer is no, so I asked to make sure

[Tzu-Ching Yen]

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.

[Victor Ivrii]

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.