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Homework Help: 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
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