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(Steps Shown) Find the characteristic coordinates \zeta, η for (cos ^2 x_2- sin ^2 x_2) (partial^2 u)/(∂ x_1^2)+2 cos x_2 (partial^2 u)/(∂ x_1)

Question: Find the characteristic coordinates \(\zeta, \eta\) for \(\left(\cos ^{2} x_{2}-\sin ^{2} x_{2}\right) \frac{\partial^{2} u}{\partial x_{1}^{2}}+2 \cos x_{2} \frac{\partial^{2} u}{\partial x_{1} \partial x_{2}}+\frac{\partial^{2} u}{\partial x_{2}^{2}}+u=0\)

Rewrite the equation in terms of \(\zeta, \eta\).

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