how to solve pde r+10s+25t =0

Question : solve pde r+10s+25t =0Solution :Given PDEr+10s+25t =0we know the notation\[r=\frac{\partial^2z}{\partial x^2},\ s=\frac{\partial^2z}{\partial x\partial y}\ ,\ t=\frac{\partial^2z}{\partial y^2} \]Hence the given PDE becomes\[\frac{\partial^2z}{\partial x^2}+10\frac{\partial^2z}{\partial x\partial y}+25\frac{\partial^2z}{\partial y^2}=0\]Which Is also a Homogeneous Linear PDE with constant coefficients.To solve this PDE…

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