Mathematics

Problem

The differential equation

y''-4y=0

has general solution

y=C_1e^{2x}+C_2e^{-2x}

. Which of the following sets of additional information is sufficient to determine both

C_1

and

C_2

uniquely? a)

y(0)=5\text{ and }y(0)=1

y(0)=2\text{ and }y''(0)=8

y(0)=3\text{ and }y'(0)=0

y(0)=3

only