An extension of Liénard’s graphical construction
and this latter equation is ordinarily interpreted as specifying a field of directions in the x — v (phase) plane; the direction, dv/dx, at point P = (x0, v0) is the slope of the solution curve through that point evaluated at P and is, from (2), equal to —j(x0))/va . The classical Li6nard construction [1, pp. 31-36] deals only with the particular case where j(x) is linear in x. Under this hypothesis and with proper scaling of the coordinates x and v, we may write (2) in the standard Lienard form: