Answer to Question #29585 in Differential Equations for Maria

Question

Let y(x) satisfy the ordinary differential equation

d^2y/dx^2 - (a^2)y = f(x)

where a>0, and y(x) tends rapidly to zero as x tends to +/- ∞. Show that the Fourier transform ŷ(k) of y(x) is given by

ŷ(k) = - f^(k)/(k^2+a^2)

(in the line above f^(k) is supposed to be f-hat(k), sorry couldn't find the right symbol)