how to solve the following Homogeneous Linear PDE with constant Coefficients

Question 1: Solve the following Homogeneous Linear PDEs with constant Coefficients \[3\frac{\partial^2z}{\partial x^2}+2\frac{\partial^2z}{\partial x\partial y}-5\frac{\partial^2z}{\partial y^2}=0\] Solution : Given PDE\[3\frac{\partial^2z}{\partial x^2}+2\frac{\partial^2z}{\partial x\partial y}-5\frac{\partial^2z}{\partial y^2}=0 \]Is a Homogeneous Linear PDE with constant coefficients.To solve such equations we process as followsStep 1:…

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