11.5.4.25 With Constant CoEFICIENTS

Condition: find everything \ (\ alpha \), in which there is a linear replacement of variables \ ((x, y) \ rightarrow (t, z) \), translating the equation \ [u_ {x} +4 u_ {x y}-\ alpha u_ {y y}-\ alphaa u_ {x}+\ alpha^{2} u_ {y} = 0 \] - in the string equation \ (u_ {t t} = u_ {z z} \); - in the equation of thermal conductivity \ (u_ {t} = u_ {z z} \).