Problem

(a) For the initial value problem (12) of Example 9, show that are solutions. Hence, this initial value problem has multiple solutions. (See also Group Project G in Chapter 2.)

b) Does the initial value problem y = 3y2/3 , y(0) = 10-7, have a unique solution in a neighborhood of x = 0?

Step 1</p>

a)Given

We have to check these are the solutions of the initial value problem,…..(1)

We have

Substituting values of and in equation (1)

We get ,

Step 2 </p>

Substitute the values of in (1) we get,

Both and satisfy the given equation .Therefore both are solutions.Hence this initial value problem has multiple solutions.