y=c1sin x + c2cos x is a solution to y''+y=0.
a. determine whether there are one or more members of this family that satisfy the conditions y(0)=0 and y(pi)=0.
b. Show that the zero function, y(triple bar)0, is the only member of the family that satisfies the conditions y(0)=0 and y(pi/2)=0.

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and for b, Im unsure of what it is really asking me?

y(0)=c2, not 1
you are trying to find conditions for c1 and c2 that satisfy the conditions

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