Suppose we must solve a Bernoulli equation but we have forgotten the change of...

Suppose we must solve a Bernoulli equation

but we have forgotten the change of variables formula that converts it to a linear equation. Suppose all we remember is that the change of variables has the form

where α is a constant that depends on n. Use this change of variables to show that α = 1 − n is the only choice that gives a linear equation for dz/dt.