Show that y = uv with v(x) = exp (-1/2 ∫ p(x)

Show that y = uv with v(x) = exp (-1/2 ∫ p(x) dx) gives from the ODE y" + p(x)y' + q(x)y = 0 the ODE

u" + [q(x) - 1/4p(x)- 1/2p' (x)] u = 0,

not containing the first derivative of u.