Classification and Characteristics of Linear Equations

The general linear equation of second order can be expressed 

Typical examples occurring in chemical engineering are. Pick s second law of diffusion 

The homogeneous linear equation of second order occurs frequently. It is the special form when S = 0. In particular, when P, Q, R are constants, denoted by a, b, c, respectively, we write 

In fact, we see the discriminant (b — 4ac) appears within the quadratic equation for A 

Whereas the functions / and g are unspecified and quite arbitrary at this point, nonetheless, much can be learned by observation of the arguments, now established to be (y + Aar). Now, suppose a = 1, b = -3, and c = 2, hence — 4flc) = 1 0, so the equation is hyperbolic with roots A, = 1, A2 = 2 hence, in general we can write 

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