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!

Fundamental Solution ODE

  1. May 22, 2010 #1
    1. The problem statement, all variables and given/known data

    Verify that y1(x) = 1 and y2(x) = x^.5 are solutions of the following y y'' + (y')^.5 = 0. Then show that c1 + c2 x^.5 is not in general a solution of this equation.

    2. Relevant equations



    3. The attempt at a solution

    I was able to show that both y1 and y2 are solutions to the DE. I found the Wronskian to be 1/(2 sqrt(x)) which is not equal to zero, so I was under the impression that this would mean that the two solutions would form a fundamental set of solution. Does anyone see why c1 + c2 x^.5 isn't a solution?
     
  2. jcsd
  3. May 22, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Your ODE isn't linear.
     
  4. May 22, 2010 #3
    Does it matter if it's not linear in general? Boyce/Diprima's theorems don't seem to make note of whether or not the ODE must be linear for a set of fundamental solutions to be valid.
     
  5. May 22, 2010 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I'd have to see the theorem, but linearity is the property that tells you if y1 and y2 are solutions to an ODE then so is c1*y1+c2*y2. I think you need it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fundamental Solution ODE
  1. Solution to an ODE (Replies: 7)

  2. ODE solution (Replies: 2)

Loading...