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Help with Differential Equation Problem

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Help with Differential Equation Problem!!!!!

1. Homework Statement
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. Homework 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!!!!
 

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