The differential equation d^2y/dx^2 = y has the general solution y(x) = A e^x + B e^(-x) (equivalently expressible using hyperbolic functions as y(x) = cosh(x) + k sinh(x) when y(0) = 1), where the constants are determined by applying the given boundary/initial conditions.
The general solution to d^2y/dx^2 = y is y(x) = A e^x + B e^(-x). Applying y(0) = 1 gives A + B = 1....
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