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