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Mathematics LibreTexts

2.2: Quasilinear Equations

Here we consider the equation


The inhomogeneous linear equation


is a special case of (\ref{quasi}).

One arrives at characteristic  equations \(x'=a_1,\ y'=a_2,\ z'=a_3\)  from (\ref{quasi}) by the same arguments as in the case of homogeneous linear equations in two variables. The additional equation \(3\) follows from


see also Section 2.3, where the general case of nonlinear equations in two variables is considered.