Let and be two solutions on of the differential equation

,such that , and , . Let be the function defined by

.(a) Show that is also a solution of .

(b) Suppose . Show that for all .

I've managed to do part (a) and the part . However, I have difficulty in proving that using the condition stated in part (b) in order to show that using the existence and uniqueness theorem. Could anyone help with this?

Thanks in advance.