Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: ODE (linear vs. nonlinear)

  1. Mar 9, 2010 #1
    In class, my teacher gave the following equations as examples of linear and nonlinear ODE. In the first equation, there are x's in front of some of the y's yet it is linear. In the second equation, there is an x in front of y^2 yet it is nonlinear - why? Also, why is the final equation nonlinear?


    x^2 y''' + (x-1)*y'' + sin(x)*y' + 5*y = tan(x)


    y' + x*y^2 = 0
    y'' + sin(x+y) = sin(x)
  2. jcsd
  3. Mar 9, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    They are linear because they are first degree in the dependent variable and its derivatives. No y2, ey, etc., and the same for y', y'' etc.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook