I'm following an example for the separation of varibales method from a book and they went from

$\displaystyle Y_1 '' -pi^2 Y_1 = 0$

$\displaystyle Y_2 '' -4pi^2 Y_2 = 0$

to

$\displaystyle Y_1 (y) = Acosh(pi*y) + B_1 sinh(2pi*y)$

$\displaystyle Y_2 (y) = A_2 cosh(2pi*y) + B_2 sinh(2pi*y)$

Can someone explain how they made that jump?

Thanks