Im studying the wave equation with Neumann boundary conditions, and got stuck at the following. can anyone help out?

i have the following equation:

T''(t) = lambda * (c^2)*T(t)

where lamba = - (n*pi*c/l)^2

i want to see how :

T''(t) = lambda * (c^2)*T(t) reduces to...

T(t) = Asin(lambda*t) + Bcos (lamdba*t)

where did the sin and cos come from? is this solved by separation of variables?i tried every way but cant understand.

thanks for reading.