Can anyone help with the following maths question:

Show that the function:

u(t,x)=f(y), where y=((2x)/sqrt(t))

is a solution of the heat equation:

partialderivative(u) / partialderivative(t) = partialderivative(u)^2 / partialderivative(x)^2

(where the partialderivative(u or x)^2 is the second derivative)

provided that f(y) satisfies 8f''(y) + yf'(y)=0

Thanks in advance!