Easy Seperable Differential Equation Domain Questions

[danerape]

This is a problem from the Boyce and Diprima Elementary DE book. I solved this equation
and got the correct solution. However, the author notes that the solution is defined on the
interval (-2,3) only. I have found it to be defined (-inf,-2)u(-2,3)u(3,inf), or EVERYWHERE BUT x=-2, x=3. Is this a mistake in the book or am I missing something?


PDF ATTACHED
Thanks a lot,

Dane

 

[HallsofIvy]

Yes, the book is correct. There exist solutions for x< -2 and x> 3 but they cannot be "connected" to the solution between -2 and 3. The solution satisfying the given boundary condition is valid only between -2 and 3.