11.5.4.25 With constant coefficients

condition: Find all \( \alpha \) for which there is a linear change of variables \( (x, y) \rightarrow(t, z) \), transforming the equation \[ u_{x x}+4 u_{x y}-\alpha u_{y y}-\alpha u_{x}+\alpha^{2} u_{y}=0 \] - into the string equation \( u_{t t}=u_{z z} \); - into the heat conduction equation \( u_{t}=u_{z z} \).