Question dealing with solving a basic IVP, posted below shortly.

Question

mendicant_bias · Answer

"Find a member of the family that is a solution of the initialvalue
problem."$$y=c_{1}e^{x}+c_{2}e^{-x}, \ \ \ (-\infty, \infty), \ \ \ y''-y=0, \ \ \ y(0)=0,\ y'(0)=1$$

mendicant_bias · Answer

@ganeshie8 , could you help me out on this?

mendicant_bias · Answer

$$y(0)=0=c_{1}e^{x}+c_{2}e^{-x}; $$$$\frac{d}{dx}\Bigg(c_{1}e^{x}+c_{2}e^{-x}\Bigg)=c_{1}e^{x}-c_{1}e^{-x}$$$$y'(0)=1=c_{1}e^{x}-c_{2}e^{-x}$$

mendicant_bias · Answer

@dan815

mendicant_bias · Answer

Second part of this problem is "Use the family in Problem 1 to find a solution of
y''-y=0 that satisfies the boundary conditions y(0)  0, y(1)  1."

mendicant_bias · Answer

I can figure out the first part, but I have no idea what the second one is asking. I'm not really sure how to solve it.