1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Are these two general solutions or one general/two particular solutions?

  1. Apr 22, 2012 #1

    s3a

    User Avatar

    1. The problem statement, all variables and given/known data
    The problem and its answers are attached.

    I prefer the first one as (same thing but isolated for y):

    y_1(x) = [k_1 * x + x * ln(x)]/[k2 - ln(x)]


    2. Relevant equations
    First order homogeneous differential equation.
    y = xv, dy/dx = v + x dv/dx


    3. The attempt at a solution
    I solved this successfully. Given that at some point in the solution of the problem for solving y_1(x), I get a denominator with (x+y), it is my "mathematical duty" to check if x + y = 0 => y = -x is a solution to the differential equation and it is. Because of the nature in which I got this y = -x solution, I am confused as to whether I treat this as one of the two alternatives for a general solution or both together span the one and only general solution.

    Any input would be greatly appreciated!
    Thanks in advance!
     

    Attached Files:

  2. jcsd
  3. Apr 22, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Your equation isn't linear, is it? It has a y^2 in it. That would mean a linear combination of solutions isn't necessarily a solution.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Are these two general solutions or one general/two particular solutions?
  1. General solution (Replies: 1)

  2. General solution (Replies: 2)

  3. General solutions (Replies: 3)

Loading...