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!

Help with Differential Equation Problem

  1. Apr 6, 2008 #1
    Help with Differential Equation Problem!!!!!

    1. The problem statement, all variables and given/known data
    The problem is shown as:
    Consider the differential equation dy/dt = (y)^(1/4), y>=0.
    (a) Find all points in the (t,y) plane through which at least one solution passes. Give reasons for your answer.
    (b) Prove that there is a unique solution to the differential equation that satisfies y(0) = 3. Note that you should not try to find the solution to answer this part of the question
    (c) Find 2 solutions to the IVP consisting of the differential equation above with the initial condition y(1)=0.
    2. Relevant equations



    3. The attempt at a solution
    I have only got this solution and have no idea about what to do with part (a) and (b) of this question.
    dy/dt = (y)^(1/4)
    (y)^(-1/4) dy/dt = 1
    (y)^(-1/4) dy = 1 dt
    int (y)^(-1/4) dy = int 1 dt
    (4/3)(y)^(3/4) = t + C
    (y)^(3/4) = (3/4)t + C
    y = [ (3/4)t + C ]^(4/3)

    Using the intial condition y(1) = 0 I got the c value as -(3/4). So I've only got one solution to this prob in the form y = [(3/4)t - (3/4)]^(4/3) and I can't find anything similar to part (a) and (b) anywhere in the text. HELP PLEASE!!!!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?