Change of variable in differential equation

Hello,

I am dealing with the following partial differential equation for the
function T(r,t):

diff( T, t ) - T^2 / r^2 * diff( ( r^2 * T^(sigma) * diff(T, r) + q / T ), r
) = 0

I now want to introduce a new variable

eta = r / t^(1/3)

and a new function

Psi(eta) = t^(1/3) * T^(1+sigma)

and I would like Maxima to transform the partial differential equation for
T(r,t) stated herebove into a differential equation for Psi(eta).

Can anyone help me with this please?

Thank you,
Wilfried