1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Early Diff EQ Solving Methods (Chp 1 status yo)

  1. Feb 12, 2013 #1
    Alright, got a quick differential equation question.

    So far in my DE class, we have learned 3 methods of solving ODE's
    -Separation of Variables
    -"Guessing" (the y=yh+yp method)
    -Integrating Factors

    How do you know when to use these methods and when not to? I understand the methods to use each of these three (Although guessing is still pretty sketchy when it comes to actually guessing).

    Does it have something to do with linearity? Or is it simply just which ever method is "nicer"? I know with integrating factors sometimes you end up with integrals that are impossible to solve, so in that case, you'd need to resort to guessing.
  2. jcsd
  3. Feb 12, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I would look at the problem and ask myself, in this order:

    1. Is if first order? If so then
    2. Is it constant coefficient? If so use the characteristic equation and ##y_h,\, y_p## if it is non-homogeneous.
    3. Is it linear? If so solve by integrating factor.
    4. Is it separable? If so separate and integrate.
    5. Write it as M(x,y)dx + N(x,y)dy = 0. Is it exact? Homogeneous (y = ux substitution)? Is there an integrating factor function of x or function of y?
    6. Is it some special equation like a Bernoulli nonlinear equation?

    Now if it is second order then:
    7. Is it constant coefficient? f so use the characteristic equation and ##y_h,\, y_p## if it is non-homogeneous.
    8. Is the ##y'## term missing? If so let ##u=y'## making a first order equation in ##y'##.
    9. Do you know one solution so you can reduce the order?
    10. Is it linear, maybe solvable by series?

    That should get you started. You usually won't have to go all the way down the list.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Early Diff Solving Date
Diff eq with constants.. Eulers identity.. Saturday at 3:32 PM
Thomson Scattering In the Early Universe May 16, 2017
Early Abstract Algebra Problem - Pinter's Textbook Aug 11, 2012
Early Calc2 HW Help Oct 25, 2007
Early Linear Algebra Sep 12, 2006