Author Topic: Linear differential equations  (Read 1424 times)

Zifeng Zhu

  • Newbie
  • *
  • Posts: 2
  • Karma: 0
    • View Profile
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

  • Full Member
  • ***
  • Posts: 16
  • Karma: 11
    • View Profile
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

  • Newbie
  • *
  • Posts: 2
  • Karma: 0
    • View Profile
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

  • Full Member
  • ***
  • Posts: 31
  • Karma: 22
    • View Profile
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 »

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 2563
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Re: linear differential equations
« Reply #4 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.
« Last Edit: September 19, 2018, 06:26:09 AM by Victor Ivrii »