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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!!!!

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# Homework Help: Help with Differential Equation Problem

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