Chapter 4.1, Problem 11E

1. (a) 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.
2. (b) The DE in part (a) has the alternative general solution y = c₃ cosh x + c₄ sinh x on (−∞, ∞). Use this family to find a solution that satisfies the boundary conditions in part (a).
3. (c) Show that the solutions in parts (a) and (b) are equivalent

1. $\begin{array}{l}y=c_1{e}^x+c_2{e}^{-x},(-\infty ,\infty );\\ y^{″}-y=0,y(0)=0,y^{\prime }(0)=1\end{array}$