The general form of \(2^{nd}\) order linear homogeneous PDE is
\(\displaystyle A(x)\phi_{xx}+B(x)\phi_{xy}+C(x)\phi_{yy}+D(x)\phi_{x}+E(x)\phi_{y}+F(x)\phi=0\)
where \(A(x),B(x),C(x),D(x),E(x),F(x)\) are the function of \(x\), and \(\phi_{xx}\) stands for \(\displaystyle\frac{\partial^{2}\phi}{\partial x^{2}}\), \(\phi_{x}\) stands for \(\displaystyle\frac{\partial\phi}{\partial x}\), etc.
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